Preparation

Load Packages

Import data

  • This is a dataset of fish catch for the North Delta Flow Action.
  • Merge flow data into rest of data
  • Define variable structures
  • Order action phases
  • Regional assignments
Fish_ndfa <- read.csv("Data/FISH_MAN_allIEPsurveys_20200527.csv")
FlowDesignation <- read.csv("Data/FlowDatesDesignations.csv")
Regions <- read.csv("Data/Stations_Fish_NDFA_2020-05-28.csv")

# Look at data
head(Fish_ndfa)
str(Fish_ndfa)

# Add variables
Fish_ndfa$Date <- ymd(Fish_ndfa$Date)
Fish_ndfa$Month <- month(Fish_ndfa$Date)
Fish_ndfa$Day <- day(Fish_ndfa$Date)
Fish_ndfa$Year <- ordered(Fish_ndfa$Year)
FlowDesignation$Year <- ordered(FlowDesignation$Year)
FlowDesignation$PreFlowStart <- mdy(FlowDesignation$PreFlowStart)
FlowDesignation$PreFlowEnd <- mdy(FlowDesignation$PreFlowEnd)
FlowDesignation$PostFlowStart <- mdy(FlowDesignation$PostFlowStart)
FlowDesignation$PostFlowEnd <- mdy(FlowDesignation$PostFlowEnd)

# Merge data from FlowDesignation Table (Water Year Type, Flow days and type)
# Filter only Pre-During-Post Flow Action Data. 
# We have a during action, and then Pre = 30 days before/Post = 30 days after
Fish_all0 <- inner_join(Fish_ndfa,FlowDesignation, by = "Year")
Fish_all1 <- left_join(Fish_all0, Regions)
Fish_all <- Fish_all1 %>%
   mutate(ActionPhase = ifelse(Date > PreFlowStart & Date<PreFlowEnd, "Pre", NA)) %>%
   mutate(ActionPhase = replace(ActionPhase, Date > PreFlowEnd & Date < PostFlowStart, "During")) %>% 
   mutate(ActionPhase = replace(ActionPhase, Date > PostFlowStart & Date < PostFlowEnd, "Post")) %>%
  filter(!is.na(ActionPhase)) %>%
   select(-c(PreFlowStart:PostFlowEnd)) %>%
   arrange(Date, Survey, StationCode, CommonName)


# Order Action Phases
Fish_all$ActionPhase <- as.factor(Fish_all$ActionPhase)
Fish_all$ActionPhase <-  factor(Fish_all$ActionPhase, levels(Fish_all$ActionPhase)[c(3,1,2)])

# Define variable structures
Fish_all$Date <- ymd(Fish_all$Date)
Fish_all$Month <- ordered(Fish_all$Month)
Fish_all$Year <- ordered(Fish_all$Year)
Fish_all$WYType <- as.factor(Fish_all$WYType)
Fish_all$ActionPhase <- as.factor(Fish_all$ActionPhase)
Fish_all$X1 <- NULL

Plotting Functions

## FUNCTIONS FOR PLOTTING -------------------------------------------------------------
VisPoint <-  function(data,y) {
    y <- enquo(y)
  data %>%
    ggplot() +
    geom_point(mapping = aes(Date,!! y), size = 2) +
    theme_bw() +
  scale_colour_manual(values = c("coral3", "lightseagreen"))+
  theme_bw() + 
  theme(panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        axis.line = element_line(colour = "black"),
        plot.title = element_text(hjust=0.5),
        axis.text = element_text(size = 11), 
        axis.text.x = element_text(angle = 90, hjust = 1),
        axis.title = element_text(size = 12),
        legend.text = element_text(size = 11),
        legend.position = "bottom")
} 

# Boxplots by variable of interest
VisBox <-  function(data, x, y) {
    x <- enquo(x)
    y <- enquo(y)
  data %>%
    ggplot() +
    geom_boxplot(mapping = aes(!! x,!! y), fill = "lightseagreen", colour = "lightgray") +
    theme_bw() +
  scale_colour_manual(values = c("coral3", "lightseagreen"))+
  theme_bw() + 
  theme(panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        axis.line = element_line(colour = "black"),
        plot.title = element_text(hjust=0.5),
        axis.text = element_text(size = 11), 
        axis.text.x = element_text(angle = 90, hjust = 1),
        axis.title = element_text(size = 12),
        legend.text = element_text(size = 11))
} 
#----------------------------------------------------------------------------------------------------
####################################################################################################

Exploration of overall dataset

  • Station distribution
  • Time span
  • Number of fish per survey
  • Total counts per survey
  • Locations
library(leaflet)
library(plotly)
# Look at locations

# Define palette
pal <- colorFactor(c("slateblue", "darkseagreen", "orange", "orangered", "hotpink"), domain = c("DJFMP", "Yolo", "Townet", "EDSM", "FMWT"))

leaflet(Fish_all) %>%
  addTiles() %>%
  addCircleMarkers(
    color = ~pal(Survey),
    opacity = 0.5,
    lng = ~Longitude,
    lat = ~Latitude,
    label = ~StationCode) %>%
  addLegend(pal = pal,
            values = ~Survey,
            position = "bottomright")
# Time span 
time <- Fish_all%>%
  group_by(Survey, Year) %>%
  summarize(sum.count = sum(totalCount))
ggplot(time, aes(x = Survey, y = Year, fill = sum.count)) + geom_tile() + theme_minimal()

# Look at datasets
Fishsp <- Fish_all %>%
  group_by(CommonName) %>% summarize(count = n())

Fish_all %>%
  plot_ly(x = ~Survey,
          y = ~totalCount,
          type = "box")
Fishsp %>%
  plot_ly(x = ~CommonName, 
          y = ~count,
          type = "bar")

Datasets by fish type

  • Make some lists of datasets you might want to filter from the big dataset

Seine Data

Data Prep

  • Filter to just seine data
  • Fill in zeros for unlisted species
  • Calculate CPUE
  • Organize data the way you want it
### Complete Cases
# For each Date, Survey, StationCode combination, make sure each fish species is represented with 
# either positive count or zero. 
Seine_completecase <- Seine %>%
  group_by(Date, Survey, StationCode, CommonName) %>%
  summarize(sum.count = sum(totalCount)) %>%
  ungroup() %>%
  complete(CommonName, nesting(Date, Survey, StationCode), fill = list(sum.count = 0)) %>%
  arrange(Date,Survey, StationCode,CommonName)

### Merge back together with rest of data

# Get distinct samples for looking at Water Quality 
Seine_samples <- Seine %>% select(-c(CommonName, totalCount)) %>% distinct()

# Merge 
Seine_complete <- left_join(Seine_completecase, Seine_samples, by = c("Date", "Survey", "StationCode"))
# There is a Yolo sample with two volumes... this is why there are more rows of Seine_complete

### Calculate CPUE
# Remove samples with no volume 
Seine_CPUE <- Seine_complete %>%
  filter(!is.na(VolumeSampled))%>%
  mutate(CPUE = round(sum.count/VolumeSampled,2))

### Rearrange columns 
Seine_f <- Seine_CPUE[, c("Date", "Year", "Month", "Day", "Survey", "StationCode", 
                          "Latitude", "Longitude", "Region", "MethodCode",
                         "WYType", "FlowPulseType", "NetFlowDays","ActionPhase", 
                         "Secchi", "Turbidity", "Conductivity", "WaterTemp", "DO", "Tow",
                         "Depth", "VolumeSampled",  "CommonName", "sum.count", "CPUE")]

### Mean CPUE 
## Calculate means for each species by year-location-actionphase
CPUE_means_seine_phase <- Seine_f %>%
  group_by(Year, Survey, StationCode, ActionPhase, CommonName) %>% 
  summarize(mean.CPUE = mean(CPUE)) 

Data Exploration

Water Quality

  • Simple point plots and histograms, correlation matrix
############ OUTLIERS #################
# Boxplots
WTvis1 <- VisPoint(Seine_samples, WaterTemp)
WTvis2 <- VisBox(Seine_samples, Month, WaterTemp)
WTvis3 <- VisBox(Seine_samples, Year, WaterTemp)
Cvis1 <- VisPoint(Seine_samples, Conductivity)
Cvis2 <- VisBox(Seine_samples, Month, Conductivity)
Cvis3 <- VisBox(Seine_samples, Year, Conductivity)
Svis1 <- VisPoint(Seine_samples, Secchi)
Svis2 <- VisBox(Seine_samples, Month, Secchi)
Svis3 <- VisBox(Seine_samples, Year, Secchi)
Tvis1 <- VisPoint(Seine_samples, Turbidity)
Tvis2 <- VisBox(Seine_samples, Month, Turbidity)
Tvis3 <- VisBox(Seine_samples, Year, Turbidity)
DOvis1 <- VisPoint(Seine_samples, DO)
DOvis2 <- VisBox(Seine_samples, Month, DO)
DOvis3 <- VisBox(Seine_samples, Year, DO)

# Plot together
grid.arrange(WTvis1, WTvis2, WTvis3, Cvis1, Cvis2, Cvis3, Svis1, Svis2, Svis3, 
             Tvis1, Tvis2, Tvis3, DOvis1, DOvis2, DOvis3, ncol = 3)

# Boxplots
plot_ly(data = Seine_samples, x = ~StationCode, y = ~WaterTemp, color = ~StationCode, type = 'box')
plot_ly(data = Seine_samples, x = ~StationCode, y = ~Conductivity, color = ~StationCode, type = 'box')
plot_ly(data = Seine_samples, x = ~StationCode, y = ~Secchi, color = ~StationCode, type = 'box')
plot_ly(data = Seine_samples, x = ~StationCode, y = ~Turbidity, color = ~StationCode, type = 'box')
plot_ly(data = Seine_samples, x = ~StationCode, y = ~DO, color = ~StationCode, type = 'box')
############ CORRELATIONS ####################
# Correlation Matrix WQ
Corr.wq <- Seine_samples %>% select(WaterTemp, Conductivity, Secchi, Turbidity, DO)
ggpairs(Corr.wq)

# Variance Inflation Factor (VIF)
corvif(Corr.wq) # Want to get rid of the variable if VIF > 4
## 
## 
## Variance inflation factors
## 
##                  GVIF
## WaterTemp    1.108283
## Conductivity 1.688919
## Secchi       1.566020
## Turbidity    1.484982
## DO           1.709443

Clean up WQ data (QC)

  • Edit anything that needs to be removed, flagged, changed.
  • Replace Missing Data
# Clean up wq data
# QC Check - does anything look weird?
Seine_samples %>% filter(WaterTemp>40 | WaterTemp<1)
##         Date Survey StationCode MethodCode Secchi Conductivity Turbidity   DO
## 1 2018-10-15  DJFMP      LI004E       SEIN     NA        153.3      16.3 9.17
##   WaterTemp Year Tow Depth VolumeSampled Latitude Longitude Month Day WYType
## 1      50.6 2018  NA   0.7            63 38.26514 -121.6716    10  15     BN
##   FlowPulseType NetFlowDays             Region ActionPhase
## 1         MA-Ag          30 CacheSloughComplex        Post
Seine_samples %>% filter(Secchi > 0.95)
##         Date Survey StationCode MethodCode Secchi Conductivity Turbidity   DO
## 1 2011-08-31   Yolo          YB      BSEIN      1         1157        NA 4.03
##   WaterTemp Year Tow Depth VolumeSampled Latitude Longitude Month Day WYType
## 1      20.7 2011   1    NA         172.5 38.56538  -121.631     8  31      W
##   FlowPulseType NetFlowDays      Region ActionPhase
## 1            NF          63 CentralYolo      During
Seine_samples %>% filter(Conductivity > 4000)
##          Date Survey StationCode MethodCode Secchi Conductivity Turbidity   DO
## 1  2012-10-19  DJFMP      MS001N       SEIN     NA         4112        NA 6.19
## 2  2014-08-19  DJFMP      MS001N       SEIN     NA         4739      5.54 8.85
## 3  2014-09-05  DJFMP      MS001N       SEIN     NA         4985     19.50 8.98
## 4  2014-09-16  DJFMP      MS001N       SEIN     NA         4903      4.48 8.22
## 5  2014-09-30  DJFMP      MS001N       SEIN     NA         5727      5.53 9.29
## 6  2014-10-09  DJFMP      MS001N       SEIN     NA         7770     10.80 9.13
## 7  2015-07-23  DJFMP      MS001N       SEIN     NA         6099      8.02 7.27
## 8  2015-08-04  DJFMP      MS001N       SEIN     NA         7904      7.85 8.01
## 9  2015-08-11  DJFMP      MS001N       SEIN     NA         7116     13.50 8.82
## 10 2015-08-18  DJFMP      MS001N       SEIN     NA         5992     10.20 6.30
## 11 2015-08-25  DJFMP      MS001N       SEIN     NA         6139     25.00 8.73
## 12 2015-09-03  DJFMP      MS001N       SEIN     NA         6260      9.19 8.84
## 13 2015-09-17  DJFMP      MS001N       SEIN     NA         7579      5.62 5.96
## 14 2015-09-24  DJFMP      MS001N       SEIN     NA         8118     18.60 8.61
## 15 2015-09-29  DJFMP      MS001N       SEIN     NA         4469     18.10 9.97
## 16 2015-10-06  DJFMP      MS001N       SEIN     NA         7618     12.30 6.23
## 17 2015-10-14  DJFMP      MS001N       SEIN     NA         6975      5.22 5.51
## 18 2015-10-20  DJFMP      MS001N       SEIN     NA         6740     15.90 6.28
## 19 2015-10-27  DJFMP      MS001N       SEIN     NA         6507      3.25 7.68
##    WaterTemp Year Tow Depth VolumeSampled Latitude Longitude Month Day WYType
## 1       19.1 2012  NA   0.7         31.85 38.05604 -121.7856    10  19     BN
## 2       21.2 2014  NA   0.9         36.00 38.05604 -121.7856     8  19      C
## 3       20.9 2014  NA   0.9         28.35 38.05604 -121.7856     9   5      C
## 4       20.5 2014  NA   0.9         31.50 38.05604 -121.7856     9  16      C
## 5       20.7 2014  NA   0.8         28.80 38.05604 -121.7856     9  30      C
## 6       20.8 2014  NA   0.5          8.75 38.05604 -121.7856    10   9      C
## 7       22.8 2015  NA   0.6         13.50 38.05604 -121.7856     7  23      C
## 8       21.8 2015  NA   0.3          9.00 38.05604 -121.7856     8   4      C
## 9       22.7 2015  NA   0.8         28.80 38.05604 -121.7856     8  11      C
## 10      23.0 2015  NA   0.6          9.00 38.05604 -121.7856     8  18      C
## 11      21.0 2015  NA   0.7         29.40 38.05604 -121.7856     8  25      C
## 12      21.1 2015  NA   0.7         18.90 38.05604 -121.7856     9   3      C
## 13      20.1 2015  NA   0.5         12.00 38.05604 -121.7856     9  17      C
## 14      21.2 2015  NA   0.7         29.40 38.05604 -121.7856     9  24      C
## 15      19.6 2015  NA   0.4          3.20 38.05604 -121.7856     9  29      C
## 16      20.1 2015  NA   0.8         31.20 38.05604 -121.7856    10   6      C
## 17      20.6 2015  NA   0.5         12.50 38.05604 -121.7856    10  14      C
## 18      19.2 2015  NA   0.8         50.40 38.05604 -121.7856    10  20      C
## 19      18.6 2015  NA   0.6         21.00 38.05604 -121.7856    10  27      C
##    FlowPulseType NetFlowDays        Region ActionPhase
## 1             CA          38 LowerSacRiver        Post
## 2             NF          15 LowerSacRiver         Pre
## 3             NF          15 LowerSacRiver         Pre
## 4             NF          15 LowerSacRiver      During
## 5             NF          15 LowerSacRiver        Post
## 6             NF          15 LowerSacRiver        Post
## 7             NF          42 LowerSacRiver         Pre
## 8             NF          42 LowerSacRiver         Pre
## 9             NF          42 LowerSacRiver         Pre
## 10            NF          42 LowerSacRiver         Pre
## 11            NF          42 LowerSacRiver      During
## 12            NF          42 LowerSacRiver      During
## 13            NF          42 LowerSacRiver      During
## 14            NF          42 LowerSacRiver      During
## 15            NF          42 LowerSacRiver      During
## 16            NF          42 LowerSacRiver        Post
## 17            NF          42 LowerSacRiver        Post
## 18            NF          42 LowerSacRiver        Post
## 19            NF          42 LowerSacRiver        Post
Seine_f$WaterTemp[Seine$WaterTemp == 50.6] <- NA

# Function to fill in missing values with mean 
impute.mean <- function(x) replace(x, is.na(x), mean(x, na.rm = TRUE))

# Filling in missing values using impute.mean function from above. 
# Variables are renamed because using mutate adds on new columns to the matrix.
# Use impute.mean to fill in NAs, rename updated variables using mutate
Seine_f <- Seine_f %>%
  group_by(WYType) %>%
  mutate(
    Cond = impute.mean(Conductivity),
    WTemp = impute.mean(WaterTemp),
    SecDepth = impute.mean(Secchi),
    Turb = impute.mean(Turbidity),
    DOx = impute.mean(DO)) %>%
  ungroup()

Data Analysis (Seine data)

  1. Filter for species or sets of species
list_nmds <- c("Sacramento Pikeminnow", "Splittail", "Hitch", "Hardhead", "Sacramento Sucker", "Sacramento Blackfish",
               "Wakasagi", "Inland Silverside", "Delta Smelt", 
               "Carp", "Goldfish", "Hardhead", "Golden Shiner", "Fathead Minnow", "Hitch",
               "Rainwater Killifish", "Western Mosquitofish", "Black Crappie", "White Crappie", "Bluegill", "Bigscale Logperch",
               "Largemouth Bass", "Smallmouth Bass", "Striped Bass", "Spotted Bass",
               "Threadfin Shad", "American Shad")
list_nmds_small <- c("Sacramento Pikeminnow", "Splittail", "Hitch", "Hardhead", "Sacramento Sucker", "Sacramento Blackfish",
               "Wakasagi", "Inland Silverside", "Delta Smelt", "Longfin Smelt", 
               "Largemouth Bass", "Smallmouth Bass", "Striped Bass", "Spotted Bass",
               "Threadfin Shad", "American Shad", "Bluegill", "Black Crappie", "Bigscale Logperch")

Seine_tf <- Seine_f %>% filter(CommonName == "Threadfin Shad")
Seine_sucker <- Seine_f %>% filter(CommonName == "Sacramento Sucker")
Seine_lmb <- Seine_f %>% filter(CommonName == "Largemouth Bass")
Seine_black <- Seine_f %>% filter(CommonName == "Sacramento Blackfish")
Seine_pike <- Seine_f %>% filter(CommonName == "Sacramento Pikeminnow")
Seine_natives <- Seine_f %>%filter(CommonName %in% list_native)
Seine_nmds_larger <- Seine_f%>% filter(CommonName %in%list_nmds)
Seine_nmds_0 <- Seine_f %>% filter(CommonName %in% list_nmds_small)

Univariate Analyses

Parametric Analyses

T-test

*Data must (approximatley) fit a known statistical model

*Highly used and have a long history

*Measures the difference in population means

  1. Independent sample t-test (two sample t-test or students t-test)
    • determines whether there is a statistically significant difference between the means in two unrelated groups
    • example: Whether first year graduate salaries differed based on gender
  2. Paired t-test
    • compares two population means where you have two samples in which observations in one sample can be paired with observations in the other sample.
    • example: Before and after measurments on the same subjects
  3. One-sample t-test
    • used to determine whether a sample comes from a population with a specific mean
    • example: You sample 1000 doctors and see if their hours differ from 100 hours.
### 1. Independent-samples t-test: Is there a difference in LMB CPUE by survey? ----------------
(lmb.ttest <- t.test(Seine_lmb$CPUE~Seine_lmb$Survey)) # not significant
## 
##  Welch Two Sample t-test
## 
## data:  Seine_lmb$CPUE by Seine_lmb$Survey
## t = 0.97697, df = 1362.2, p-value = 0.3288
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.002880479  0.008596023
## sample estimates:
## mean in group DJFMP  mean in group Yolo 
##          0.01439474          0.01153696
# Plot
ggplot(Seine_lmb, aes(x = Survey, y = CPUE)) + geom_boxplot()

ggplot(Seine_lmb, aes(x = CPUE, color = Survey)) + geom_density()

ggplot(Seine_lmb, aes(x = Survey, y = CPUE)) + geom_col() # This works best for data with lots of zeros

### 2. Paired t-test: Does a treatment cause a difference? Did Action Phase alter CPUE of LMB? -------------
Seine_lmb2 <-  filter(Seine_lmb, ActionPhase!="During")
(lmb.ttest2 <- t.test(Seine_lmb2$CPUE ~ Seine_lmb2$ActionPhase)) # significant
## 
##  Welch Two Sample t-test
## 
## data:  Seine_lmb2$CPUE by Seine_lmb2$ActionPhase
## t = 2.0514, df = 542.51, p-value = 0.04071
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.0004562724 0.0210537512
## sample estimates:
##  mean in group Pre mean in group Post 
##        0.019175050        0.008420039
# Plot: Figure out the direction of the trend
ggplot(Seine_lmb2, aes(x = ActionPhase, y = CPUE)) + geom_boxplot()

ggplot(Seine_lmb2, aes(x = CPUE, color = ActionPhase)) + geom_density()

ggplot(Seine_lmb2, aes(x = ActionPhase, y = CPUE)) + geom_col() # This works best for data with lots of zeros

### 3. One-sample t-test: Is the CPUE greater than 0? ---------------------------------------
(lmb.ttest3 <- t.test(Seine_lmb$CPUE, mu = 0)) # p < 0.05, Yes, it is
## 
##  One Sample t-test
## 
## data:  Seine_lmb$CPUE
## t = 6.9746, df = 1653, p-value = 4.42e-12
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  0.009708318 0.017304984
## sample estimates:
##  mean of x 
## 0.01350665

ANOVA

Run ANOVA
  1. One-way
    • used to determine whether there are any statistically significant differences between the means of two or more independent (unrelated) groups (although you tend to only see it used when there are a minimum of three).
  2. Two-way
    • used to compare the mean differences between groups that have been split on two independent variables (called factors). The primary purpose of a two-way ANOVA is to understand if there is an interaction between the two independent variables on the dependent variable.
### 1. One-way ANOVA: Effect of action phase on Threadfin Shad CPUE
(tf.aov1 <- aov(CPUE~ActionPhase, data = Seine_tf))
## Call:
##    aov(formula = CPUE ~ ActionPhase, data = Seine_tf)
## 
## Terms:
##                 ActionPhase Residuals
## Sum of Squares       2.4957  329.6404
## Deg. of Freedom           2      1651
## 
## Residual standard error: 0.4468345
## Estimated effects may be unbalanced
summary(tf.aov1)
##               Df Sum Sq Mean Sq F value  Pr(>F)   
## ActionPhase    2    2.5  1.2478    6.25 0.00198 **
## Residuals   1651  329.6  0.1997                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
### 2. Two-way ANOVA: Effect of action phase and water year type on Threadfin Shad CPUE
(tf.aov2 <- aov(CPUE~ActionPhase + Region, data = Seine_tf))
## Call:
##    aov(formula = CPUE ~ ActionPhase + Region, data = Seine_tf)
## 
## Terms:
##                 ActionPhase   Region Residuals
## Sum of Squares       2.4957   5.3135  324.3269
## Deg. of Freedom           2        3      1648
## 
## Residual standard error: 0.4436218
## Estimated effects may be unbalanced
summary(tf.aov2)
##               Df Sum Sq Mean Sq F value   Pr(>F)    
## ActionPhase    2    2.5  1.2478   6.341  0.00181 ** 
## Region         3    5.3  1.7712   9.000 6.52e-06 ***
## Residuals   1648  324.3  0.1968                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
### If both significant, check interaction.
(tf.aov3 <- aov(CPUE~ActionPhase + Region, data = Seine_tf))
## Call:
##    aov(formula = CPUE ~ ActionPhase + Region, data = Seine_tf)
## 
## Terms:
##                 ActionPhase   Region Residuals
## Sum of Squares       2.4957   5.3135  324.3269
## Deg. of Freedom           2        3      1648
## 
## Residual standard error: 0.4436218
## Estimated effects may be unbalanced
summary(tf.aov3)
##               Df Sum Sq Mean Sq F value   Pr(>F)    
## ActionPhase    2    2.5  1.2478   6.341  0.00181 ** 
## Region         3    5.3  1.7712   9.000 6.52e-06 ***
## Residuals   1648  324.3  0.1968                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Test Assumptions
  • Plot results, can use statistical tests to check if desired but pretty sensitive.
  1. Residuals are normally distributed
  2. Residuals are homogeneous across groups
library(car)

# Test for normality of residuals
par(mfrow = c(1,1))
plot(tf.aov2,2)

tf.resid <- residuals(object = tf.aov2)
shapiro.test(tf.resid) # p < 0.05 means not normal
## 
##  Shapiro-Wilk normality test
## 
## data:  tf.resid
## W = 0.38605, p-value < 2.2e-16
# Test for homogeneity of variance. 
# If data are normal: Bartlett's test
# If data are nonnnormal or Fligner-Killeen Test: Levene's test (In this case, use this one)
plot(tf.aov2, 1)

bartlett.test(CPUE~interaction(ActionPhase,Region), data = Seine_tf) #p<0.05 means they are NOT homogeneous
## 
##  Bartlett test of homogeneity of variances
## 
## data:  CPUE by interaction(ActionPhase, Region)
## Bartlett's K-squared = 776.73, df = 11, p-value < 2.2e-16
leveneTest(CPUE~ActionPhase*Region, data = Seine_tf) #p<0.05 means they are NOT homogeneous
## Levene's Test for Homogeneity of Variance (center = median)
##         Df F value    Pr(>F)    
## group   11  4.6714 4.613e-07 ***
##       1642                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Post-Hoc Tests

P-Value Corrections: * Tukey: set family error rate * Bonferroni: divide p-value by number of comparisons * Holm-Bonferroni : sequential bonferroni, more powerful than bonferroni

library(lsmeans)
library(multcomp)
library(multcompView)
leastsquare.tf = lsmeans(tf.aov2, 
                         ~ActionPhase|Region,
                         adjust = "holm")

# Compact letter display - test each comparison
(CLD <- cld(leastsquare.tf, alpha = 0.05, Letters = letters, adjust = "holm"))
## Region = CacheSloughComplex:
##  ActionPhase   lsmean     SE   df lower.CL upper.CL .group
##  Post        -0.00621 0.0260 1648  -0.0686   0.0562  a    
##  Pre          0.05046 0.0251 1648  -0.0097   0.1106  ab   
##  During       0.09917 0.0232 1648   0.0436   0.1547   b   
## 
## Region = CentralYolo:
##  ActionPhase   lsmean     SE   df lower.CL upper.CL .group
##  Post         0.12596 0.0239 1648   0.0687   0.1832  a    
##  Pre          0.18263 0.0255 1648   0.1216   0.2436  ab   
##  During       0.23134 0.0240 1648   0.1739   0.2887   b   
## 
## Region = LowerSacRiver:
##  ActionPhase   lsmean     SE   df lower.CL upper.CL .group
##  Post         0.10833 0.0328 1648   0.0296   0.1870  a    
##  Pre          0.16501 0.0326 1648   0.0870   0.2430  ab   
##  During       0.21372 0.0312 1648   0.1389   0.2886   b   
## 
## Region = LowerYolo:
##  ActionPhase   lsmean     SE   df lower.CL upper.CL .group
##  Post         0.09384 0.0297 1648   0.0226   0.1651  a    
##  Pre          0.15052 0.0303 1648   0.0780   0.2230  ab   
##  During       0.19923 0.0285 1648   0.1309   0.2676   b   
## 
## Confidence level used: 0.95 
## Conf-level adjustment: bonferroni method for 3 estimates 
## P value adjustment: holm method for 3 tests 
## significance level used: alpha = 0.05
Plot Results
library(FSA)

# One plot idea
pd = position_dodge(0.4)    ### How much to jitter the points on the plot

ggplot(CLD,
       aes(x     = Region,
           y     = lsmean,
           color = ActionPhase,
           label = .group)) +

    geom_point(shape  = 15,
               size   = 4,
             position = pd) +

    geom_errorbar(aes(ymin  =  lower.CL,
                      ymax  =  upper.CL),
                      width =  0.2,
                      size  =  0.7,
                      position = pd) +

    theme_bw() +
    theme(axis.title   = element_text(face = "bold"),
          axis.text    = element_text(face = "bold"),
          plot.caption = element_text(hjust = 0)) +

    ylab("Mean CPUE") +
     ggtitle ("Mean Threadfin Shad CPUE",
            subtitle = "By Region and Action Phase") +
 
            labs(caption  = paste0("\nInterpretation ",
                                   "here \n"),
                            hjust=0.5) +
 
  geom_text(nudge_x = c(0.1, -0.1, 0.1, -0.1, 0.1, -0.1, -0.1, 0.1),
            nudge_y = c(0.1,  0.05, 0.05,  0.05, 0.05 , 0.05,  0.05, 0.05),
            color   = "black") +
 
  scale_color_manual(values = c("blue", "red", "green"))

# Graphics
# Using standard error
# Need to manually insert the lsmeans significant groupings

Sum.tf = Summarize(CPUE~ActionPhase + Region, data = Seine_tf, digits = 3)
Sum.tf$se = Sum.tf$sd/sqrt(Sum.tf$n)
Sum.tf$se = signif(Sum.tf$se, digits = 3)

#levels(Sum.tf$Season) <- c("Dry 2015", "Wet", "Dry 2016")

ggplot(Sum.tf, aes(x = Region, y = mean, color = ActionPhase)) +
  geom_errorbar(aes(ymin = mean-se,
                    ymax = mean +se),
                width = 0.2, size = 0.7, position = position_dodge(0.2)) +
  geom_point(aes(shape = ActionPhase), size = 4, position = position_dodge(0.2)) +
  # annotate("text", x = 1, y = 5.5, label = "e", size = 6) +
  # annotate("text", x = 1.15, y = 3.8, label = "de", size = 6) +
  # annotate("text", x = 1.1, y = 2.5, label = "bcd", size = 6) +
  # annotate("text", x = 1.85, y = 0.6, label = "ab", size = 6) +
  # annotate("text", x = 2, y = 1, label = "ab", size = 6) +
  # annotate("text", x = 2.2, y = 0.65, label = "abc", size = 6) +
  # annotate("text", x = 2.9, y = 0.45, label = "a", size = 6) +
  # annotate("text", x = 3.05, y = 0.4,label = "ab", size=6) +
  # annotate("text", x = 3.2, y = 4, label = "cde", size = 6) +
  labs(y = expression(paste("Mean CPUE (ind   ", m^{-3},")")))+
  theme_bw() +
  theme(axis.title = element_text(face = "bold"),
        axis.text = element_text(size = 14),
        legend.text = element_text(size = 13)) +
  scale_colour_manual(values = c("#1db918", "#2e8fad", "#e52078"))

ANCOVA

*ANCOVA is a blend of analysis of variance (ANOVA) and regression. It is similar to factorial ANOVA, in that it can tell you what additional information you can get by considering one independent variable (factor) at a time, without the influence of the others.

Non-parametric Analyses

Kruskal-Wallis: only for one factor

library(lattice)
# Check distributions are similar
histogram(~CPUE  | ActionPhase,
          data = Seine_tf,
          layout = c(1,3))

boxplot(CPUE~ActionPhase,
        data = Seine_tf, 
        ylab = "ActionPhase",
        xlab = "CPUE")

kruskal.test(CPUE~ActionPhase, data = Seine_tf)
## 
##  Kruskal-Wallis rank sum test
## 
## data:  CPUE by ActionPhase
## Kruskal-Wallis chi-squared = 18.372, df = 2, p-value = 0.0001025

Post-hoc for Kruskal-Wallis * Dunn Test: Appropriate for groups with unequal numbers of observations (Zar 2010) * Nemenyi test: Not appropriate for groups with unequal numbers of observations (Zar 2010) * Pairwise Mann-Whitney U

library(FSA)
library(rcompanion)
## Warning: package 'rcompanion' was built under R version 3.6.3
### Dunn
(tf.dunn <- dunnTest(CPUE~ActionPhase, 
                    data = Seine_tf,
                    method = "holm"))
## Dunn (1964) Kruskal-Wallis multiple comparison
##   p-values adjusted with the Holm method.
##      Comparison         Z      P.unadj        P.adj
## 1 During - Post  4.151433 3.303995e-05 9.911985e-05
## 2  During - Pre  2.796070 5.172820e-03 1.034564e-02
## 3    Post - Pre -1.244619 2.132718e-01 2.132718e-01
# Get the letters wit compact letter display
tf.res <- tf.dunn$res
cldList(comparison = tf.res$Comparison,
        p.value = tf.res$P.adj,
        threshold = 0.05)
##    Group Letter MonoLetter
## 1 During      a         a 
## 2   Post      b          b
## 3    Pre      b          b

Kolmogorov-Smirnov Test

  • Are two distributions different from each other?
  • Lower D statistic = more probable that samples came from same distribution. If D >1, more likely they are not from the same distribution
  • Can follow up to ask if one is larger than the other
  • Example: Compare size distributions from Male vs. Female fish
  • Here: Compare CPUE distributions from Threadfin Shad vs. Inland Silverside
# ECDF and K-S TEST
TF <- filter(Seine_f, CommonName=="Threadfin Shad")
ISS <- filter(Seine_f, CommonName == "Inland Silverside")
ks.test(TF$CPUE, ISS$CPUE)
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  TF$CPUE and ISS$CPUE
## D = 0.47582, p-value < 2.2e-16
## alternative hypothesis: two-sided
# Plot cumulative distribution
# Plot data (CPUE) from least to greatest.
Seine_ecdf <- filter(Seine_f, CommonName %in% c("Threadfin Shad", "Inland Silverside"))
ggplot(Seine_ecdf, aes(CPUE, color=CommonName)) +
  stat_ecdf() +
  labs(x= "CPUE",
       y = "Cumulative Probability",
       title = "ISS and Threadfin Shad") +
  theme_bw() +
  annotate("text", x=100, y=0.7, label="D = 0.47582", size=6) +
  annotate("text", x =100, y = 0.625, label = "p < 0.05", size = 5)

Goodness of Fit

Chi Square

  • How does the observed value differ from expected value?

General Linear Model Code

  1. Check out data - what kind of distribution does this look like?
  • If there are a lot of zeros, you might want to look at zero-inflated possion or negative binomial
  1. Scale and center continuous variables if very different
  2. Run full model (all variables)
  3. Run alternate models, or run dredge to run all possible model combinations
  4. Use AIC to pick best model
  5. Check model
library(MuMIn)
## Warning: package 'MuMIn' was built under R version 3.6.3
library(pscl)
## Warning: package 'pscl' was built under R version 3.6.3
## Classes and Methods for R developed in the
## Political Science Computational Laboratory
## Department of Political Science
## Stanford University
## Simon Jackman
## hurdle and zeroinfl functions by Achim Zeileis
library(AER)
## Warning: package 'AER' was built under R version 3.6.3
## Loading required package: lmtest
## Warning: package 'lmtest' was built under R version 3.6.3
## Loading required package: zoo
## Warning: package 'zoo' was built under R version 3.6.3
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
## Loading required package: sandwich
## Warning: package 'sandwich' was built under R version 3.6.3
# Look at distribution of data - is it zero-inflated?
ggplot(Seine_tf, aes(CPUE)) + geom_histogram(binwidth = 0.1) + theme_bw()

plot_ly(data = Seine_tf, x = ~Survey, y = ~CPUE,  type = 'box')
# Scale and center continuous variables if needed
Seine_tf_scale <- Seine_tf %>%
  mutate(Turb2 = scale(Turb, center = TRUE),
         Cond2 = scale(Cond, center = TRUE),
         WTemp2 = scale(WTemp),
         DOx2 = scale(DOx))

# For CPUE, use offset to account for sampling effort
Seine_tf_scale$Samp <- log(Seine_tf_scale$VolumeSampled)

# Start with normal poisson
L0 <- glm(sum.count ~ Region + ActionPhase + WYType + Survey + Turb2 + Cond2 + WTemp2 + DOx2 +
            offset(Samp), family = poisson, data = Seine_tf_scale)
TF.back <- step(L0, direction = "backward")
## Start:  AIC=41271.96
## sum.count ~ Region + ActionPhase + WYType + Survey + Turb2 + 
##     Cond2 + WTemp2 + DOx2 + offset(Samp)
## 
##               Df Deviance   AIC
## <none>              38657 41272
## - ActionPhase  2    39051 41662
## - Turb2        1    39061 41673
## - Survey       1    39074 41687
## - DOx2         1    39471 42083
## - WYType       3    39864 42472
## - Region       3    40411 43020
## - WTemp2       1    40442 43055
## - Cond2        1    40597 43210
summary(TF.back)
## 
## Call:
## glm(formula = sum.count ~ Region + ActionPhase + WYType + Survey + 
##     Turb2 + Cond2 + WTemp2 + DOx2 + offset(Samp), family = poisson, 
##     data = Seine_tf_scale)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -15.692   -3.175   -1.983   -1.109   37.795  
## 
## Coefficients:
##                      Estimate Std. Error  z value Pr(>|z|)    
## (Intercept)         -3.416158   0.032489 -105.147   <2e-16 ***
## RegionCentralYolo    1.139674   0.029577   38.533   <2e-16 ***
## RegionLowerSacRiver  0.893184   0.039886   22.394   <2e-16 ***
## RegionLowerYolo      0.734504   0.031858   23.055   <2e-16 ***
## ActionPhaseDuring    0.330513   0.019436   17.005   <2e-16 ***
## ActionPhasePost     -0.032401   0.026298   -1.232    0.218    
## WYTypeC             -0.343248   0.028815  -11.912   <2e-16 ***
## WYTypeD             -0.379042   0.032456  -11.679   <2e-16 ***
## WYTypeW              0.353282   0.019860   17.789   <2e-16 ***
## SurveyYolo           0.478734   0.023978   19.965   <2e-16 ***
## Turb2                0.141655   0.006244   22.687   <2e-16 ***
## Cond2                0.346987   0.006445   53.841   <2e-16 ***
## WTemp2               0.389507   0.007605   51.218   <2e-16 ***
## DOx2                 0.224957   0.007746   29.043   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for poisson family taken to be 1)
## 
##     Null deviance: 50134  on 1653  degrees of freedom
## Residual deviance: 38657  on 1640  degrees of freedom
## AIC: 41272
## 
## Number of Fisher Scoring iterations: 7
par(mfrow = c(2,2))
plot(TF.back)

# Check for overdispersion. Overdispersed if >1: Use NB
dispersiontest(TF.back, trafo = 1)
## 
##  Overdispersion test
## 
## data:  TF.back
## z = 4.529, p-value = 2.963e-06
## alternative hypothesis: true alpha is greater than 0
## sample estimates:
##    alpha 
## 68.37969
### Model: zero-inflated poisson -------------------------------
# You can only have full count data, not CPUE.
# Need to add the offset! 

f1 <- formula(sum.count ~ Region + ActionPhase + WYType + Survey + 
                Turb2 + Cond2 + WTemp2 + DOx2 + offset(Samp))
zip1 <- zeroinfl(f1, dist = "poisson", link = "logit", data = Seine_tf_scale); summary(zip1)
## 
## Call:
## zeroinfl(formula = f1, data = Seine_tf_scale, dist = "poisson", link = "logit")
## 
## Pearson residuals:
##      Min       1Q   Median       3Q      Max 
## -10.8393  -0.6789  -0.4068  -0.2389  90.2956 
## 
## Count model coefficients (poisson with log link):
##                      Estimate Std. Error z value Pr(>|z|)    
## (Intercept)         -2.001944   0.034460 -58.096  < 2e-16 ***
## RegionCentralYolo    1.422792   0.031522  45.137  < 2e-16 ***
## RegionLowerSacRiver  1.151508   0.043151  26.685  < 2e-16 ***
## RegionLowerYolo      0.967594   0.033533  28.855  < 2e-16 ***
## ActionPhaseDuring    0.152665   0.020211   7.553 4.24e-14 ***
## ActionPhasePost     -0.211540   0.030858  -6.855 7.12e-12 ***
## WYTypeC             -0.332060   0.029205 -11.370  < 2e-16 ***
## WYTypeD             -0.568581   0.032777 -17.347  < 2e-16 ***
## WYTypeW              0.098849   0.020282   4.874 1.09e-06 ***
## SurveyYolo          -0.679347   0.025096 -27.070  < 2e-16 ***
## Turb2                0.122576   0.009340  13.124  < 2e-16 ***
## Cond2                0.243778   0.006649  36.664  < 2e-16 ***
## WTemp2               0.333656   0.011298  29.531  < 2e-16 ***
## DOx2                 0.244617   0.008503  28.770  < 2e-16 ***
## 
## Zero-inflation model coefficients (binomial with logit link):
##                     Estimate Std. Error z value Pr(>|z|)    
## (Intercept)         -1.87377    0.20243  -9.256  < 2e-16 ***
## RegionCentralYolo   -0.10339    0.19509  -0.530 0.596120    
## RegionLowerSacRiver  0.42717    0.23509   1.817 0.069209 .  
## RegionLowerYolo      0.22528    0.22667   0.994 0.320274    
## ActionPhaseDuring   -0.59641    0.16439  -3.628 0.000286 ***
## ActionPhasePost     -0.56218    0.22875  -2.458 0.013988 *  
## WYTypeC              0.05927    0.19173   0.309 0.757210    
## WYTypeD             -0.23081    0.24653  -0.936 0.349150    
## WYTypeW             -0.76708    0.16676  -4.600 4.23e-06 ***
## SurveyYolo          -3.14038    0.18631 -16.855  < 2e-16 ***
## Turb2               -0.49948    0.08989  -5.557 2.75e-08 ***
## Cond2               -0.13145    0.06227  -2.111 0.034774 *  
## WTemp2              -0.43138    0.09326  -4.626 3.74e-06 ***
## DOx2                 0.13556    0.07280   1.862 0.062597 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Number of iterations in BFGS optimization: 33 
## Log-likelihood: -1.385e+04 on 28 Df
### Model: zero-inflated negative binomial -------------------------------------
zinb1 <- zeroinfl(f1, na.action = "na.fail", dist="negbin", link = "logit", data = Seine_tf_scale);summary(zinb1)
## 
## Call:
## zeroinfl(formula = f1, data = Seine_tf_scale, na.action = "na.fail", 
##     dist = "negbin", link = "logit")
## 
## Pearson residuals:
##     Min      1Q  Median      3Q     Max 
## -0.5840 -0.4136 -0.2359 -0.1020 44.8409 
## 
## Count model coefficients (negbin with log link):
##                     Estimate Std. Error z value Pr(>|z|)    
## (Intercept)         -2.62884    0.23659 -11.111  < 2e-16 ***
## RegionCentralYolo    1.97135    0.23190   8.501  < 2e-16 ***
## RegionLowerSacRiver  1.09760    0.35102   3.127 0.001767 ** 
## RegionLowerYolo      1.34225    0.24399   5.501 3.77e-08 ***
## ActionPhaseDuring    0.56227    0.16805   3.346 0.000821 ***
## ActionPhasePost     -0.18972    0.21401  -0.886 0.375371    
## WYTypeC              0.15510    0.18335   0.846 0.397603    
## WYTypeD             -0.77634    0.24079  -3.224 0.001264 ** 
## WYTypeW              0.06992    0.15780   0.443 0.657716    
## SurveyYolo          -0.90083    0.19718  -4.568 4.91e-06 ***
## Turb2                0.07749    0.05788   1.339 0.180613    
## Cond2                0.28758    0.11655   2.467 0.013607 *  
## WTemp2               0.55053    0.08920   6.172 6.76e-10 ***
## DOx2                 0.40450    0.08701   4.649 3.34e-06 ***
## Log(theta)          -1.07104    0.06002 -17.844  < 2e-16 ***
## 
## Zero-inflation model coefficients (binomial with logit link):
##                     Estimate Std. Error z value Pr(>|z|)    
## (Intercept)         -3.07706    0.43776  -7.029 2.08e-12 ***
## RegionCentralYolo   -0.15714    0.37221  -0.422  0.67289    
## RegionLowerSacRiver -0.06357    0.39943  -0.159  0.87356    
## RegionLowerYolo      0.27803    0.52446   0.530  0.59602    
## ActionPhaseDuring   -0.86203    0.30955  -2.785  0.00536 ** 
## ActionPhasePost     -2.68552    0.48653  -5.520 3.40e-08 ***
## WYTypeC             -0.06660    0.36540  -0.182  0.85536    
## WYTypeD             -0.62095    0.47342  -1.312  0.18965    
## WYTypeW              0.31395    0.36392   0.863  0.38831    
## SurveyYolo          -5.86023    1.39824  -4.191 2.78e-05 ***
## Turb2               -3.46293    0.41888  -8.267  < 2e-16 ***
## Cond2               -0.18549    0.13541  -1.370  0.17072    
## WTemp2              -0.64932    0.23542  -2.758  0.00581 ** 
## DOx2                 0.84448    0.17597   4.799 1.59e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Theta = 0.3427 
## Number of iterations in BFGS optimization: 43 
## Log-likelihood: -3237 on 29 Df
### Dredge function runs all the available models to tell you what the best model is.
# AIC within 2 = about the same model
# Pick what makes sense for your system, or average your top models

# Use AIC to pick the best models, then look at variables that aren't significant, and re-run model without significant variables
# m1.dredge <- dredge(zinb1)

# Take out survey (not significant)
f2 <- formula(sum.count ~ Region + ActionPhase + WYType + Turb2 + Cond2 + WTemp2 + DOx2)
zinb2 <- zeroinfl(f2, na.action = "na.fail", dist="negbin", link = "logit", data = Seine_tf_scale) ; summary(zinb2)
## 
## Call:
## zeroinfl(formula = f2, data = Seine_tf_scale, na.action = "na.fail", 
##     dist = "negbin", link = "logit")
## 
## Pearson residuals:
##       Min        1Q    Median        3Q       Max 
##  -0.55796  -0.42419  -0.19052  -0.07899 142.94954 
## 
## Count model coefficients (negbin with log link):
##                     Estimate Std. Error z value Pr(>|z|)    
## (Intercept)          1.35650    0.22904   5.922 3.17e-09 ***
## RegionCentralYolo    1.71465    0.20156   8.507  < 2e-16 ***
## RegionLowerSacRiver  1.02258    0.28378   3.603 0.000314 ***
## RegionLowerYolo      0.89870    0.19020   4.725 2.30e-06 ***
## ActionPhaseDuring    0.54012    0.17069   3.164 0.001555 ** 
## ActionPhasePost     -0.12232    0.21834  -0.560 0.575331    
## WYTypeC             -0.13793    0.18066  -0.763 0.445169    
## WYTypeD             -0.73700    0.23984  -3.073 0.002120 ** 
## WYTypeW              0.18007    0.15517   1.160 0.245864    
## Turb2                0.04757    0.05738   0.829 0.407131    
## Cond2                0.10714    0.06102   1.756 0.079116 .  
## WTemp2               0.52062    0.08650   6.019 1.76e-09 ***
## DOx2                 0.35866    0.08936   4.013 5.98e-05 ***
## Log(theta)          -1.16228    0.05565 -20.887  < 2e-16 ***
## 
## Zero-inflation model coefficients (binomial with logit link):
##                      Estimate Std. Error z value Pr(>|z|)    
## (Intercept)          -8.24798    1.42708  -5.780 7.49e-09 ***
## RegionCentralYolo     0.18055    0.41380   0.436  0.66260    
## RegionLowerSacRiver   0.35358    0.44042   0.803  0.42207    
## RegionLowerYolo      -1.01985    0.39302  -2.595  0.00946 ** 
## ActionPhaseDuring     0.31230    0.34216   0.913  0.36139    
## ActionPhasePost      -0.91380    0.43004  -2.125  0.03359 *  
## WYTypeC               1.27898    0.46025   2.779  0.00545 ** 
## WYTypeD              -0.06631    0.52887  -0.125  0.90022    
## WYTypeW              -0.20728    0.37953  -0.546  0.58497    
## Turb2                -2.49070    0.42585  -5.849 4.95e-09 ***
## Cond2               -27.17737    4.07591  -6.668 2.60e-11 ***
## WTemp2               -0.01475    0.16854  -0.087  0.93028    
## DOx2                 -0.13506    0.18753  -0.720  0.47140    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Theta = 0.3128 
## Number of iterations in BFGS optimization: 50 
## Log-likelihood: -3197 on 27 Df
m2.dredge <- dredge(zinb2)
## Fixed terms are "count_(Intercept)" and "zero_(Intercept)"
## Warning in value[[3L]](cond): system is computationally singular: reciprocal
## condition number = 2.56432e-33FALSE
# Diagnostic Plots -------------------------------------
# Model Validation 
# Calculate residuals
EP1 <- resid(zinb2, type = "pearson")

# Diagnostic Plots
par(mfrow = c(2,5))
plot(x=zinb2$fitted.values, y = EP1, main = "Pearson residuals")
qqnorm(EP1)
plot(x=Seine_tf_scale$ActionPhase,y = EP1, main = "Action Phase")
plot(x=Seine_tf_scale$WYType, EP1, main = "Water Year Type")
plot(x=Seine_tf_scale$Region, EP1, main = "Water Year Type")

plot(x=Seine_tf_scale$Cond2, EP1, main = "Conductivity")
plot(x=Seine_tf_scale$WTemp2, EP1, main = "Water Temperature")
plot(x=Seine_tf_scale$Turb2, EP1, main = "Turbidity")
plot(x=Seine_tf_scale$DOx2, EP1, main = "DO")

Multivariate Analyses

Preparation

  1. Some summary stats

  2. Look for outliers in species data

  3. Look at initial trends - env. vs. species

  4. Pick transformations needed

  5. Summary Stats

snstatsall <- Seine_nmds_larger%>% 
  group_by(CommonName) %>%
  summarize(mean = mean(CPUE), 
            max = max(CPUE),
            min = min(CPUE), 
            sum = sum(CPUE),
            CV = sd(CPUE)/mean,
            zeros = sum(CPUE == 0),
            n = n(), 
            prop.absent = round(zeros/n,2))

snstats <- Seine_nmds_0 %>% 
  group_by(CommonName) %>%
  summarize(mean = mean(CPUE), 
            max = max(CPUE),
            min = min(CPUE), 
            sum = sum(CPUE),
            CV = sd(CPUE)/mean,
            zeros = sum(CPUE == 0),
            n = n(), 
            prop.absent = round(zeros/n,2))
  1. Remove certain species
  • Need to make decisions about which species to keep in
  • Species occurring in fewer than 5% samples
  • Species occurring in >95% samples
  • Species with CV (standard deviation/mean) < 10%

Here: * Remove species that are not present: Hardhead, Smallmouth Bass, Longfin Smelt * Species < 5% of samples: Hitch, Wakasagi, Delta Smelt, Sacramento Blackfish

notabund <- c("Hardhead", "Smallmouth Bass", "Longfin Smelt", "Hitch", "Wakasagi", "Delta Smelt", "Sacramento Blackfish")
Seine_nmds <- filter(Seine_nmds_0, !(CommonName %in% notabund))

Exploration/QC

  1. Look for outliers in species data
  • Click species to remove, look at each individual species for any obvious outliers
# Overall CPUE
par(mfrow = c(1,1))
index= seq(1,length(Seine_nmds$CPUE))

# Explore each species - look for outliers here by adding and removing species
Seine_nmds%>%
  plot_ly() %>%
  add_trace(x = ~index, 
            y = ~CPUE, 
            color = ~CommonName,
            colors = "Set3",
            type = "scatter")
  1. Look at initial trends - environment vs. species
# Threadfin vs environmental
threadfin1 <- ggplot(Seine_tf, aes(x = WTemp, y = CPUE)) + geom_point() + theme_bw()
threadfin2 <- ggplot(Seine_tf, aes(x = Cond, y = CPUE)) + geom_point() + theme_bw()
threadfin3 <- ggplot(Seine_tf, aes(x = Turb, y = CPUE)) + geom_point() + theme_bw()
threadfin4 <- ggplot(Seine_tf, aes(x = DOx, y = CPUE)) + geom_point() + theme_bw()
grid.arrange(threadfin1, threadfin2, threadfin3, threadfin4, top = "Threadfin CPUE by Environmental Variable")

# Sac Sucker vs environmental
sucker1 <- ggplot(Seine_sucker, aes(x = WTemp, y = CPUE)) + geom_point() + theme_bw()
sucker2 <- ggplot(Seine_sucker, aes(x = Cond, y = CPUE)) + geom_point() + theme_bw()
sucker3 <- ggplot(Seine_sucker, aes(x = Turb, y = CPUE)) + geom_point() + theme_bw()
sucker4 <- ggplot(Seine_sucker, aes(x = DOx, y = CPUE)) + geom_point() + theme_bw()
grid.arrange(sucker1, sucker2, sucker3,sucker4, top = "Sac Sucker CPUE by Environmental Variable")

# Largemouth Bass vs environmental
lmb1 <- ggplot(Seine_lmb, aes(x = WTemp, y = CPUE)) + geom_point() + theme_bw()
lmb2 <- ggplot(Seine_lmb, aes(x = Cond, y = CPUE)) + geom_point() + theme_bw()
lmb3 <- ggplot(Seine_lmb, aes(x = Turb, y = CPUE)) + geom_point() + theme_bw()
lmb4 <- ggplot(Seine_lmb, aes(x = DOx, y = CPUE)) + geom_point() + theme_bw()
grid.arrange(lmb1, lmb2, lmb3, lmb4, top = "Largemouth Bass CPUE by Environmental Variable")

Transformations

  • For highly skewed variables, and to help you meet assumptions of a statistical test
  • Can help emphasize presence/absence
  • Equalize relative importance of variabilities
  • Pick transformations that do not change the rank - power, log, arcsine, arcsine sqrt
  1. Log of sqrt for highly skewed data, or ranging >2 order magnitude
  2. Arcsine sqrt for proportional data
  3. Use same transformation for same variable set (e.g. species)
  4. Consider binary transformation when percent of zero values is high (>50%) or distinct values low (<10)
# Environmental Matrix
Seine_pca <- sample_n(Seine_nmds, 300)
Seine_env <- Seine_pca %>% dplyr::select(c(26:30))

# Check for normality of variables
cond <- Seine_env$Cond
temp <- Seine_env$WTemp
sd <- Seine_env$SecDepth
turb <- Seine_env$Turb
do <- Seine_env$DOx

hist(cond)

hist(log(cond+1)) # Use this

qqnorm(log(cond+1))

hist(temp)

hist(log(temp+1)) # Use this

hist(sqrt(temp))

qqnorm(temp)

qqnorm(log(temp+1))

hist(sd) # Keep it?

hist(log(sd+1))

qqnorm(sd)

qqnorm(log(sd+1))

hist(turb)

hist(sqrt(turb))

hist(log(turb+1))

qqnorm(log(turb+1)) # Use this

hist(do) # Keep it

qqnorm(do)

PCA

Run PCA

  1. Apply transformations
  2. If you have variables with different units/scales, choose the correlation matrix (scale = TRUE). Then you do not need to scale your data beforehand.
  3. Run PCA
  4. Check PCA (Scree plot, Randomization Tests)
source('biostats.R')
library(vegan)
library(ggfortify)

### Transform to get close to normality assumptions
Seine_env_t <- Seine_env %>% mutate(Cond = log(Cond + 1),
                                    WTemp = log(WTemp + 1),
                                    Turb = log(Turb + 1)) %>%
  as.data.frame()

row.names(Seine_env_t) <- row.names(Seine_env_t)

### Run PCA. Center and Scale the data (correlation matrix).
pca.env <- prcomp(Seine_env_t, center=T, scale.=T)
summary(pca.env)
## Importance of components:
##                          PC1    PC2    PC3    PC4     PC5
## Standard deviation     1.317 1.1461 0.9140 0.8168 0.67001
## Proportion of Variance 0.347 0.2627 0.1671 0.1334 0.08978
## Cumulative Proportion  0.347 0.6097 0.7768 0.9102 1.00000
### Check how well PCA worked
# Scree Plot with Broken Stick values. 
# If eigenvalue is greater than broken stick value it is "significant"
screeplot(pca.env, bstick = TRUE) # According to this, don't keep PC1 and PC2

# Monte Carlo Randomization
# This is slow. Ideally, have several dimensions (up to number of variables) to look at trend.
# ordi.monte(Seine_env_t, ord = 'pca', dim = 5) # According to this, keep PC1 and PC2

### Check which variables matter
# Loadings. Generally, if magnitude >/= 0.3 this is important.
pca.env$rotation
##                 PC1         PC2        PC3       PC4        PC5
## Cond      0.6375704 -0.08878988  0.1256680 0.2657685 -0.7065374
## WTemp     0.3131169 -0.52724578 -0.6590205 0.2772202  0.3358729
## SecDepth -0.2411527 -0.57264653  0.6119790 0.4689510  0.1395991
## Turb      0.4193001  0.55067114  0.2139776 0.4545542  0.5182112
## DOx      -0.5113655  0.28803732 -0.3599927 0.6526726 -0.3161702
# Structure coefficients: linear correlations between original variables and PC scores
pca.structure(pca.env, Seine_env_t, dim = 5, cutoff = 0.4)
## 
## Structure Correlations:
##             PC1    PC2    PC3   PC4    PC5
## Cond       0.84                     -0.473
## WTemp     0.412 -0.604 -0.602             
## SecDepth        -0.656  0.559             
## Turb      0.552  0.631                    
## DOx      -0.674               0.533

Plot

  1. Plot and interpret PCA
# Autoplot has best customization, looks nice
  # use the "data = " to bring in original dataset so we can 
  # color-code by factors
autoplot(pca.env, data = Seine_pca, colour = 'ActionPhase', loadings = TRUE,
         loadings.label = TRUE,
         loadings.colour = "black",
         loadings.label.vjust = -.5,
         loadings.label.col = "black",
         loadings.label.size = 4,
         loadings.label.font = 4) +
  theme_bw()

autoplot(pca.env, data = Seine_pca, colour = 'WYType', loadings = TRUE,
         loadings.label = TRUE,
         loadings.colour = "black",
         loadings.label.vjust = -.5,
         loadings.label.col = "black",
         loadings.label.size = 4,
         loadings.label.font = 4) + 
  theme_bw()

NMDS

Prep

  1. Pick your variables
  2. Switch to wide format (species listed across the top)
  3. Remove any row where nothing was caught
Matrix
Seine_f_sp <- Seine_nmds %>% dplyr::select(c("Survey", "StationCode", "Date", "FlowPulseType", "WYType",
                                    "ActionPhase", "Region", "Month", "CommonName", "CPUE", "Cond",
                                    "WTemp", "SecDepth", "Turb", "DOx"))
# Species Matrix
Seine_sp_w <- Seine_f_sp %>% pivot_wider(names_from = CommonName, values_from = CPUE, values_fill = list(CPUE=0)) %>% ungroup()

# Remove any row where there is no catch for the day.
Seine_sp_sum <- Seine_sp_w %>% mutate(Total = dplyr::select(., 14:25) %>%  rowSums(na.rm = TRUE)) %>%
  filter(Total !=0)
Transform and/or standardize for nMDS
  • Some options for transformations: sqrt, log, absence/presence
# Sqrt transform data
sqrt.seine <- Seine_sp_sum %>% mutate_if(is.numeric, function(x) {
  sqrt(x)
})
                   
# Log transform data
log.seine <- Seine_sp_sum %>% mutate_if(is.numeric, function(x) {
  log(x + 1) })

# Absence/Presence data
bin.seine <- Seine_sp_sum %>% mutate_if(is.numeric, function(x) {
  case_when(x>0 ~0,
            x ==0 ~1)})

# Proportional data

Run NMDS

  1. Run
  • Currently a subset of data since otherwise even 2000 iterations won’t converge :(
  • Went with sqrt transformation - least change
library(vegan)

test.seine <- sample_n(sqrt.seine, 120)
str(test.seine)

# NMDS Seine
# This can be slow
seine.nmds <- metaMDS(test.seine[,14:25], distance="bray", k=2, trymax=500, autotransform = FALSE)
seine.nmds
  1. Check NMDS #### Interpretation
  • Stress < 0.15 is acceptable fit.
  • Check stressplot.
# Scree Plot - what should k=? 
# This can be slow
nmds.scree(test.seine[,14:25], distance='bray', k=5, trymax = 300, autotransform = FALSE) 

### Check NMDS solution 
# Large scatter is not good
stressplot(seine.nmds)

Plots!

  1. Plot Results.
### NMDS scores
seine.scores <- as.data.frame(scores(seine.nmds))

# Need a category to merge scores with the rest of env data
row.names(seine.scores) <- row.names(test.seine)
seine.nmdsplot <- cbind(seine.scores, test.seine)


# Make Plot
plot(seine.nmds)

ordiplot(seine.nmds, type = "n")
orditorp(seine.nmds, display = "species", col = "red", air = 0.01)
orditorp(seine.nmds, display = "sites", cex = 1, air = 0.01)

species.scores <- as.data.frame(scores(seine.nmds, "species"))
species.scores$species <- rownames(species.scores)
head(species.scores)
##                         NMDS1      NMDS2           species
## American Shad      0.10675580  0.1866564     American Shad
## Bigscale Logperch -0.58481110  0.5298449 Bigscale Logperch
## Black Crappie     -0.86360660  0.8683071     Black Crappie
## Bluegill          -0.76474645  0.3631291          Bluegill
## Inland Silverside -0.02075581 -0.6972043 Inland Silverside
## Largemouth Bass   -0.51293357 -0.2759583   Largemouth Bass
# Prettier Plots
# Option 1
ggplot(seine.nmdsplot, aes(NMDS1, NMDS2, color = ActionPhase)) + 
  geom_point(position = position_jitter(.1)) +
  geom_text(aes(label = WYType)) +
  stat_ellipse(type = 't', size = 1) +
  annotate("text", x = min(seine.nmdsplot$NMDS1), y = min(seine.nmdsplot$NMDS2), label = paste('Stress = ', round(seine.nmds$stress,3))) + # Add stress to plot
  theme_minimal() 

# Option 2
# With species scores and boxes

# Make the datasets for the boxes
grp.a <- seine.nmdsplot[seine.nmdsplot$ActionPhase == "Pre", ][chull(seine.nmdsplot[seine.nmdsplot$ActionPhase == 
    "Pre", c("NMDS1", "NMDS2")]), ]  # hull values for grp A
grp.b <- seine.nmdsplot[seine.nmdsplot$ActionPhase == "During", ][chull(seine.nmdsplot[seine.nmdsplot$ActionPhase == 
    "During", c("NMDS1", "NMDS2")]), ]  # hull values for grp B
grp.c<- seine.nmdsplot[seine.nmdsplot$ActionPhase == "Post", ][chull(seine.nmdsplot[seine.nmdsplot$ActionPhase == 
    "Post", c("NMDS1", "NMDS2")]), ]  # hull values for grp C
hull.data0 <- rbind(grp.a, grp.b)  #combine grp.a and grp.b
hull.data <- rbind(hull.data0,grp.c)

# Plot
ggplot() + 
  geom_point(data = seine.nmdsplot, aes(x = NMDS1, y = NMDS2, color = ActionPhase),
             position = position_jitter(.1)) +
  geom_text(data = seine.nmdsplot, aes(NMDS1, NMDS2, label = WYType, color = ActionPhase)) +
  geom_text(data = species.scores, aes(x = NMDS1, y = NMDS2, label= species), color = "black", size = 5) +
  theme_minimal() +
  annotate("text", x = min(seine.nmdsplot$NMDS1), y = min(seine.nmdsplot$NMDS2), label = paste('Stress = ', round(seine.nmds$stress,3))) + # Add stress to plot
  geom_polygon(data=hull.data,aes(x=NMDS1,y=NMDS2,fill=ActionPhase,group=ActionPhase),alpha=0.30) 

PERMANOVA

Run Models

  • You can include both continuous and categorical variables
  1. Transform continuous variables
  2. Standardize species data (basically becomes proportional data) to reduce influence of large numbers. Could also do sqrt transformation.
  3. Run PERMANOVA with each variable separately. Only keep significant variables.
  4. Create model that is significant with greatest R2, move down the list until new variables are not signficant.
  5. For any categorical variables, test interactions as well.
# Row standardization
seine.st <- data.stand(Seine_sp_sum[,14:25], method = 'total', margin = 'row', plot = F)

# Individual permanova models
(perm.WY <- adonis(formula = seine.st~WYType, data = Seine_sp_sum, method = "bray", permutations = 99))
## 
## Call:
## adonis(formula = seine.st ~ WYType, data = Seine_sp_sum, permutations = 99,      method = "bray") 
## 
## Permutation: free
## Number of permutations: 99
## 
## Terms added sequentially (first to last)
## 
##             Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)   
## WYType       3      3.09 1.02896  4.6551 0.00862   0.01 **
## Residuals 1606    354.99 0.22104         0.99138          
## Total     1609    358.08                 1.00000          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(perm.Action <- adonis(formula = seine.st~ActionPhase, data = Seine_sp_sum, method = "bray", permutations = 99))
## 
## Call:
## adonis(formula = seine.st ~ ActionPhase, data = Seine_sp_sum,      permutations = 99, method = "bray") 
## 
## Permutation: free
## Number of permutations: 99
## 
## Terms added sequentially (first to last)
## 
##               Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)   
## ActionPhase    2      2.55 1.27653  5.7701 0.00713   0.01 **
## Residuals   1607    355.52 0.22123         0.99287          
## Total       1609    358.08                 1.00000          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(perm.FlowPulse <- adonis(formula = seine.st~FlowPulseType, data = Seine_sp_sum, method = "bray", permutations = 99))
## 
## Call:
## adonis(formula = seine.st ~ FlowPulseType, data = Seine_sp_sum,      permutations = 99, method = "bray") 
## 
## Permutation: free
## Number of permutations: 99
## 
## Terms added sequentially (first to last)
## 
##                 Df SumsOfSqs MeanSqs F.Model     R2 Pr(>F)   
## FlowPulseType    3      2.18 0.72766  3.2836 0.0061   0.01 **
## Residuals     1606    355.89 0.22160         0.9939          
## Total         1609    358.08                 1.0000          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(perm.Month <- adonis(formula = seine.st~Month, data = Seine_sp_sum, method = "bray", permutations = 99))
## 
## Call:
## adonis(formula = seine.st ~ Month, data = Seine_sp_sum, permutations = 99,      method = "bray") 
## 
## Permutation: free
## Number of permutations: 99
## 
## Terms added sequentially (first to last)
## 
##             Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)   
## Month        5      6.10 1.21925  5.5562 0.01703   0.01 **
## Residuals 1604    351.98 0.21944         0.98297          
## Total     1609    358.08                 1.00000          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(perm.Survey <- adonis(formula = seine.st~Region, data = Seine_sp_sum, method = "bray", permutations = 99))
## 
## Call:
## adonis(formula = seine.st ~ Region, data = Seine_sp_sum, permutations = 99,      method = "bray") 
## 
## Permutation: free
## Number of permutations: 99
## 
## Terms added sequentially (first to last)
## 
##             Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)   
## Region       3     40.70 13.5681  68.659 0.11368   0.01 **
## Residuals 1606    317.37  0.1976         0.88632          
## Total     1609    358.08                 1.00000          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
perm.2 <- adonis(formula = seine.st~Region * Month, data = Seine_sp_sum, method = "bray", 
                 permutations = 99)
perm.2
## 
## Call:
## adonis(formula = seine.st ~ Region * Month, data = Seine_sp_sum,      permutations = 99, method = "bray") 
## 
## Permutation: free
## Number of permutations: 99
## 
## Terms added sequentially (first to last)
## 
##                Df SumsOfSqs MeanSqs F.Model      R2 Pr(>F)   
## Region          3     40.70 13.5681  70.177 0.11368   0.01 **
## Month           5      5.49  1.0986   5.682 0.01534   0.01 **
## Region:Month   15      5.24  0.3493   1.807 0.01463   0.01 **
## Residuals    1586    306.64  0.1933         0.85635          
## Total        1609    358.08                 1.00000          
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Homogeneity of Variance

  1. Test for Homogeneity of Variance
  • Choose variables in your model
  • You want the anova not to be significant (significant means variances are not homogeneous)
  • Boxplots should be pretty equal
# Make dissimilarity matrix
spe.d <- vegdist(seine.st, "bray")

# StationCode
(sp.bdp <- betadisper(spe.d, Seine_sp_sum$Region))
## 
##  Homogeneity of multivariate dispersions
## 
## Call: betadisper(d = spe.d, group = Seine_sp_sum$Region)
## 
## No. of Positive Eigenvalues: 294
## No. of Negative Eigenvalues: 787
## 
## Average distance to median:
## CacheSloughComplex        CentralYolo      LowerSacRiver          LowerYolo 
##             0.2224             0.5223             0.2023             0.3346 
## 
## Eigenvalues for PCoA axes:
## (Showing 8 of 1081 eigenvalues)
##  PCoA1  PCoA2  PCoA3  PCoA4  PCoA5  PCoA6  PCoA7  PCoA8 
## 142.59  62.00  34.55  25.24  24.39  22.07  19.02  18.54
anova(sp.bdp)
## Analysis of Variance Table
## 
## Response: Distances
##             Df  Sum Sq Mean Sq F value    Pr(>F)    
## Groups       3  29.669  9.8895  123.58 < 2.2e-16 ***
## Residuals 1606 128.519  0.0800                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
permutest(sp.bdp,pairwise=TRUE)
## 
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 999
## 
## Response: Distances
##             Df  Sum Sq Mean Sq      F N.Perm Pr(>F)    
## Groups       3  29.669  9.8895 123.58    999  0.001 ***
## Residuals 1606 128.519  0.0800                         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
##                    CacheSloughComplex CentralYolo LowerSacRiver LowerYolo
## CacheSloughComplex                     1.0000e-03    4.5000e-01     0.001
## CentralYolo                3.1020e-61                1.0000e-03     0.001
## LowerSacRiver              4.2483e-01  6.3558e-52                   0.001
## LowerYolo                  4.8538e-07  7.4989e-26    2.4494e-07
plot(sp.bdp, ellipse = TRUE)

boxplot(sp.bdp)

# Month
(sp.bdp2 <- betadisper(spe.d, Seine_sp_sum$Month))
## 
##  Homogeneity of multivariate dispersions
## 
## Call: betadisper(d = spe.d, group = Seine_sp_sum$Month)
## 
## No. of Positive Eigenvalues: 294
## No. of Negative Eigenvalues: 787
## 
## Average distance to median:
##      6      7      8      9     10     11 
## 0.5940 0.4078 0.3614 0.3455 0.3889 0.3987 
## 
## Eigenvalues for PCoA axes:
## (Showing 8 of 1081 eigenvalues)
##  PCoA1  PCoA2  PCoA3  PCoA4  PCoA5  PCoA6  PCoA7  PCoA8 
## 142.59  62.00  34.55  25.24  24.39  22.07  19.02  18.54
anova(sp.bdp2)
## Analysis of Variance Table
## 
## Response: Distances
##             Df  Sum Sq Mean Sq F value   Pr(>F)   
## Groups       5   2.006 0.40114  3.3466 0.005187 **
## Residuals 1604 192.263 0.11986                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
permutest(sp.bdp2,pairwise=TRUE)
## 
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 999
## 
## Response: Distances
##             Df  Sum Sq Mean Sq      F N.Perm Pr(>F)   
## Groups       5   2.006 0.40114 3.3466    999  0.005 **
## Residuals 1604 192.263 0.11986                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
##             6          7          8          9         10    11
## 6             0.00500000 0.00100000 0.00100000 0.00400000 0.008
## 7  0.00589699            0.16900000 0.09400000 0.59100000 0.837
## 8  0.00030353 0.17233564            0.47400000 0.22200000 0.392
## 9  0.00029747 0.08935643 0.46255086            0.08800000 0.284
## 10 0.00403739 0.61937007 0.22506651 0.08158716            0.852
## 11 0.00767118 0.87018153 0.41620055 0.27964219 0.84799411
plot(sp.bdp2, ellipse = TRUE)

boxplot(sp.bdp2)

# WYType
sp.bdp3 <- betadisper(spe.d, Seine_sp_sum$WYType)
sp.bdp3
## 
##  Homogeneity of multivariate dispersions
## 
## Call: betadisper(d = spe.d, group = Seine_sp_sum$WYType)
## 
## No. of Positive Eigenvalues: 294
## No. of Negative Eigenvalues: 787
## 
## Average distance to median:
##     BN      C      D      W 
## 0.3799 0.3255 0.4120 0.3894 
## 
## Eigenvalues for PCoA axes:
## (Showing 8 of 1081 eigenvalues)
##  PCoA1  PCoA2  PCoA3  PCoA4  PCoA5  PCoA6  PCoA7  PCoA8 
## 142.59  62.00  34.55  25.24  24.39  22.07  19.02  18.54
anova(sp.bdp3)
## Analysis of Variance Table
## 
## Response: Distances
##             Df  Sum Sq Mean Sq F value  Pr(>F)  
## Groups       3   1.263 0.42085  3.4755 0.01548 *
## Residuals 1606 194.476 0.12109                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
permutest(sp.bdp3,pairwise=TRUE)
## 
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 999
## 
## Response: Distances
##             Df  Sum Sq Mean Sq      F N.Perm Pr(>F)  
## Groups       3   1.263 0.42085 3.4755    999  0.019 *
## Residuals 1606 194.476 0.12109                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
##           BN         C         D     W
## BN           0.0320000 0.3100000 0.654
## C  0.0306297           0.0110000 0.007
## D  0.3032466 0.0097894           0.423
## W  0.6470484 0.0055393 0.4275720
plot(sp.bdp3, ellipse = TRUE)

boxplot(sp.bdp3)

# ActionPhase
sp.bdp4 <- betadisper(spe.d, Seine_sp_sum$ActionPhase)
sp.bdp4
## 
##  Homogeneity of multivariate dispersions
## 
## Call: betadisper(d = spe.d, group = Seine_sp_sum$ActionPhase)
## 
## No. of Positive Eigenvalues: 294
## No. of Negative Eigenvalues: 787
## 
## Average distance to median:
##    Pre During   Post 
## 0.4138 0.3394 0.3814 
## 
## Eigenvalues for PCoA axes:
## (Showing 8 of 1081 eigenvalues)
##  PCoA1  PCoA2  PCoA3  PCoA4  PCoA5  PCoA6  PCoA7  PCoA8 
## 142.59  62.00  34.55  25.24  24.39  22.07  19.02  18.54
anova(sp.bdp4)
## Analysis of Variance Table
## 
## Response: Distances
##             Df  Sum Sq Mean Sq F value   Pr(>F)   
## Groups       2   1.537 0.76831  6.3302 0.001826 **
## Residuals 1607 195.045 0.12137                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
permutest(sp.bdp4,pairwise=TRUE)
## 
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 999
## 
## Response: Distances
##             Df  Sum Sq Mean Sq      F N.Perm Pr(>F)   
## Groups       2   1.537 0.76831 6.3302    999  0.002 **
## Residuals 1607 195.045 0.12137                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
##               Pre     During  Post
## Pre               0.00100000 0.165
## During 0.00030026            0.062
## Post   0.15430722 0.04585440
plot(sp.bdp4, ellipse = TRUE)

boxplot(sp.bdp4)

# FlowPulseType
sp.bdp5 <- betadisper(spe.d, Seine_sp_sum$FlowPulseType)
sp.bdp5
## 
##  Homogeneity of multivariate dispersions
## 
## Call: betadisper(d = spe.d, group = Seine_sp_sum$FlowPulseType)
## 
## No. of Positive Eigenvalues: 294
## No. of Negative Eigenvalues: 787
## 
## Average distance to median:
##     CA  MA-Ag  MA-SR     NF 
## 0.3982 0.3813 0.4100 0.3582 
## 
## Eigenvalues for PCoA axes:
## (Showing 8 of 1081 eigenvalues)
##  PCoA1  PCoA2  PCoA3  PCoA4  PCoA5  PCoA6  PCoA7  PCoA8 
## 142.59  62.00  34.55  25.24  24.39  22.07  19.02  18.54
anova(sp.bdp5)
## Analysis of Variance Table
## 
## Response: Distances
##             Df  Sum Sq Mean Sq F value Pr(>F)
## Groups       3   0.619 0.20647  1.6972 0.1657
## Residuals 1606 195.367 0.12165
permutest(sp.bdp5,pairwise=TRUE)
## 
## Permutation test for homogeneity of multivariate dispersions
## Permutation: free
## Number of permutations: 999
## 
## Response: Distances
##             Df  Sum Sq Mean Sq      F N.Perm Pr(>F)
## Groups       3   0.619 0.20647 1.6972    999  0.163
## Residuals 1606 195.367 0.12165                     
## 
## Pairwise comparisons:
## (Observed p-value below diagonal, permuted p-value above diagonal)
##            CA   MA-Ag   MA-SR    NF
## CA            0.54900 0.72000 0.062
## MA-Ag 0.56724         0.45000 0.384
## MA-SR 0.72630 0.46347         0.113
## NF    0.06312 0.37808 0.10734
plot(sp.bdp5, ellipse = TRUE)

boxplot(sp.bdp5)

CCA

Run CCA

  • Format: 1 matrix of predictors, 1 matrix of species data
  1. Transform and standardize continuous variables
  2. Transform species data - sqrt
  3. Check if unimodal distribution
# Prepare continuous data
seine.env.scaled <- as.data.frame(scale(Seine_sp_sum[,9:13]),center = "TRUE", scale = "TRUE")
seine.env.f <- cbind(seine.env.scaled, Seine_sp_sum[,c("WYType", "ActionPhase", "FlowPulseType", "Month", "Region")])

# Prepare species data
seine.sp <- sqrt.seine[,14:25]

# Check unimodal distribution
# Axis length > 4 = unimodal (CCA)
# 2-4 probably unimodal
# <2 = linear model
decorana(seine.sp, ira=0)
## 
## Call:
## decorana(veg = seine.sp, ira = 0) 
## 
## Detrended correspondence analysis with 26 segments.
## Rescaling of axes with 4 iterations.
## 
##                   DCA1   DCA2   DCA3   DCA4
## Eigenvalues     0.4822 0.4194 0.2702 0.2582
## Decorana values 0.5982 0.3530 0.2407 0.1847
## Axis lengths    4.4706 5.3601 4.2156 4.3944
# Run CCA
spe.cca <- cca(seine.sp ~.,seine.env.f)
summary(spe.cca)
## 
## Call:
## cca(formula = seine.sp ~ Cond + WTemp + SecDepth + Turb + DOx +      WYType + ActionPhase + FlowPulseType + Month + Region, data = seine.env.f) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total          2.9507     1.0000
## Constrained    0.4501     0.1525
## Unconstrained  2.5006     0.8475
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1    CCA2    CCA3     CCA4    CCA5     CCA6
## Eigenvalue            0.23500 0.10254 0.04697 0.016973 0.01446 0.012272
## Proportion Explained  0.07964 0.03475 0.01592 0.005752 0.00490 0.004159
## Cumulative Proportion 0.07964 0.11439 0.13031 0.136063 0.14096 0.145123
##                           CCA7     CCA8     CCA9    CCA10     CCA11    CA1
## Eigenvalue            0.007931 0.007318 0.003741 0.002249 0.0006676 0.5052
## Proportion Explained  0.002688 0.002480 0.001268 0.000762 0.0002263 0.1712
## Cumulative Proportion 0.147811 0.150291 0.151559 0.152321 0.1525468 0.3238
##                          CA2     CA3     CA4     CA5     CA6    CA7    CA8
## Eigenvalue            0.3754 0.27933 0.25931 0.20688 0.19181 0.1800 0.1511
## Proportion Explained  0.1272 0.09466 0.08788 0.07011 0.06501 0.0610 0.0512
## Cumulative Proportion 0.4510 0.54565 0.63353 0.70364 0.76864 0.8296 0.8808
##                          CA9    CA10    CA11
## Eigenvalue            0.1378 0.11722 0.09658
## Proportion Explained  0.0467 0.03973 0.03273
## Cumulative Proportion 0.9275 0.96727 1.00000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                         CCA1   CCA2    CCA3    CCA4    CCA5    CCA6     CCA7
## Eigenvalue            0.2350 0.1025 0.04697 0.01697 0.01446 0.01227 0.007931
## Proportion Explained  0.5221 0.2278 0.10434 0.03771 0.03212 0.02726 0.017619
## Cumulative Proportion 0.5221 0.7499 0.85424 0.89195 0.92407 0.95133 0.968952
##                           CCA8     CCA9    CCA10     CCA11
## Eigenvalue            0.007318 0.003741 0.002249 0.0006676
## Proportion Explained  0.016259 0.008311 0.004996 0.0014833
## Cumulative Proportion 0.985210 0.993521 0.998517 1.0000000
## 
## Scaling 2 for species and site scores
## * Species are scaled proportional to eigenvalues
## * Sites are unscaled: weighted dispersion equal on all dimensions
## 
## 
## Species scores
## 
##                          CCA1     CCA2     CCA3      CCA4      CCA5      CCA6
## American Shad         -0.3864 -0.17890 -0.47388 -0.101298  0.166499  0.217996
## Bigscale Logperch      0.7680  0.28576 -0.05396 -0.004455  0.002668 -0.067560
## Black Crappie          1.0493  0.23224 -0.32185  0.218715 -0.120695  0.067561
## Bluegill               1.1017  0.02645  0.16278 -0.027316  0.046888  0.354338
## Inland Silverside     -0.3023  0.01871  0.07074  0.020230 -0.017381  0.007594
## Largemouth Bass        0.2968 -0.22243  0.10671 -0.032732  0.340546 -0.070658
## Sacramento Pikeminnow  0.3742 -1.10405 -0.09626  0.092479  0.145509  0.023398
## Sacramento Sucker      0.6878 -1.65347 -0.11948 -0.097490 -0.497062 -0.100904
## Splittail             -0.1431 -1.16417 -0.88934  0.611779  0.727074 -0.202490
## Spotted Bass           0.7244 -0.44496  0.86808 -0.876165  0.354275 -0.327929
## Striped Bass          -0.4953  0.19540 -0.89939 -0.453138 -0.013094  0.082728
## Threadfin Shad         0.5665  0.30668 -0.11887  0.031264 -0.035948 -0.163776
## 
## 
## Site scores (weighted averages of species scores)
## 
##              CCA1       CCA2       CCA3       CCA4       CCA5       CCA6
## row1     2.801831 -15.077967 -2.183e+00  -5.457686 -3.003e+01  -8.037389
## row2     1.251255 -10.119668 -2.406e+00   2.220662 -6.361e+00  -3.213392
## row3     1.565944  -9.871410 -2.590e+00  -0.032991 -1.537e+01  -6.458851
## row4     0.714324  -8.269205 -3.681e+00   5.848850  9.393e-01  -4.480817
## row5     1.918276 -11.228901 -1.681e+00   1.533764 -5.001e-01  -1.751285
## row6    -0.631137  -1.355018  1.206e+00   1.265470  3.282e+00  -0.064737
## row7     2.926656 -16.125005 -2.544e+00  -5.743941 -3.438e+01  -8.222299
## row8     0.515756  -6.749413 -4.029e-01   0.241897 -7.785e+00  -1.519882
## row9     0.440822  -1.967547 -3.180e+00   4.412576  5.645e+00  -4.927966
## row10   -1.092873  -1.760016 -4.669e+00   0.714328  1.071e+01   5.440877
## row11   -1.355444   0.327739 -2.351e-01  -1.159112 -1.177e+00   1.134906
## row12   -0.813767  -3.137722 -5.931e+00   6.366238  1.454e+01   0.730435
## row13   -1.016369   0.280351  4.358e-01   0.780116 -4.809e-01   0.621526
## row14   -0.298493  -2.723476 -6.411e-01   3.435126  4.661e+00  -2.185265
## row15   -1.679352   0.114469 -9.244e+00 -10.491435  3.136e+00   8.374594
## row16   -0.253190  -4.586141 -6.642e+00  11.854763  1.586e+01  -5.471308
## row17   -0.745759  -1.395362  1.093e+00   1.542830  1.874e+00   0.371502
## row18    0.636082  -3.198645 -7.696e+00  -0.351403  1.050e+01  -4.054906
## row19    0.446025  -7.782604 -5.532e+00  10.156265  1.373e+01  -7.093745
## row20    1.918328 -12.221870 -1.574e+00  -4.083867 -2.644e+01  -6.106216
## row21    1.884561 -11.997450 -1.925e+00   0.341839 -9.686e+00  -2.475135
## row22    2.553958 -12.998779 -1.465e+00  -4.889246 -2.140e+01  -7.670198
## row23    0.183237  -5.480846 -7.291e-03  -0.077185 -8.435e+00  -1.527994
## row24    1.872919  -9.862282 -9.808e-01   0.263235  1.420e+00  -3.061964
## row25    0.134183   0.648898  4.621e-01   0.931898  1.967e+00  -4.281949
## row26    2.486661   1.440051  6.075e-01   0.108152  2.440e-01   5.000734
## row27    1.830710   1.583449 -6.506e-01   2.055906 -1.582e+00   0.030031
## row28    1.561871   0.842462  6.786e-01   1.528693 -7.551e-01   7.033482
## row29    1.233995   0.462342 -3.225e-01   2.854383  1.478e+00   3.105517
## row30    1.856774   1.526880 -7.009e-01  -0.245404  3.742e-01  -0.470115
## row31    1.304059   0.959535 -2.488e+00   2.442170  1.449e+00  -2.867479
## row32    2.327052   1.465517 -1.513e-01   1.506867 -8.388e-01   3.887416
## row33    1.820491   1.075059 -1.559e+00   0.497931  2.592e-01  -0.941870
## row34    1.214001   1.836053 -2.874e+00  -1.450288 -1.338e+00  -2.198625
## row35    1.262893  -2.169212  2.272e+00  -1.928496  2.355e+01  -5.757663
## row36    2.559755   0.293565 -5.216e+00  10.500593  1.542e+00   1.143540
## row37   -0.948674   0.327594 -1.678e+00  -1.196659  4.587e-01   1.730364
## row38   -0.235468   1.111617 -3.770e+00  -2.244116 -2.218e+00   0.565620
## row39   -1.330009   0.274395  4.044e-01  -0.295670 -1.186e+00   0.945362
## row40   -0.407101  -0.833280 -3.751e+00  -0.939953  3.840e+00  -1.792494
## row41   -1.039609  -0.704069 -2.946e+00  -0.178519  2.809e+00   0.109492
## row42   -0.195846   1.010780  3.154e-01   1.383674 -1.581e+00  -3.499933
## row43   -1.157243   0.385709  3.987e-01  -0.029706 -1.246e+00   0.267109
## row44   -0.060524  -0.818665 -1.499e+00   5.452167  5.839e+00  -1.686174
## row45   -1.074017   0.682197 -1.834e+00  -2.772442 -1.274e+00   0.252763
## row46    1.262893  -2.169212  2.272e+00  -1.928496  2.355e+01  -5.757663
## row47    1.486760  -8.012405 -6.651e-01   3.085200  1.438e+01  -0.548837
## row48   -0.084741  -0.785393 -1.372e+00   2.392075  1.859e+00  -1.757738
## row49    0.222364   0.186591 -1.427e+00   2.697694  5.988e-01  -3.973122
## row50   -0.608004  -0.629808 -3.825e+00  -2.389505  2.419e+00   2.874266
## row51   -0.361687  -2.669391 -6.752e+00  -6.200573 -2.795e-01   4.004187
## row52   -0.698708  -1.056900 -1.609e+00   4.444181  3.654e+00   0.305941
## row53   -0.165915   0.957235 -3.322e+00  -1.932299  4.041e-01  -0.872637
## row54   -0.648497   0.737928 -2.632e+00  -2.271529 -1.302e-01   0.140441
## row55   -0.593396  -3.028121 -5.001e+00   4.916186  7.517e+00   0.089096
## row56    1.850612 -11.944083 -1.573e+00  -3.241833 -2.315e+01  -5.368948
## row57    0.415115  -3.986824  6.316e-01   1.548118  1.009e+01  -0.976264
## row58   -1.737626   0.184630 -1.334e+01 -13.025048  3.792e+00   2.855551
## row59    1.391919   0.003835 -1.488e+00   2.294768 -6.593e-02  -7.448801
## row60    0.481830  -6.697088 -1.270e+00   2.222232 -2.347e+00  -2.452385
## row61    1.080773  -8.308753 -5.883e-01  -1.516122 -1.184e+01  -3.544038
## row62   -0.064894  -4.545020  3.321e-01  -0.818764 -1.082e+01  -1.944216
## row63    1.710281  -9.294254 -9.697e-01   1.745970  6.808e+00  -1.708591
## row64    0.403462  -0.664840  5.571e+00 -13.073457  5.609e+00  -8.709448
## row65    2.166737 -13.073576 -2.262e+00   0.630247 -9.068e+00  -2.453885
## row66    1.314012  -9.866830 -1.058e+00  -2.352463 -1.890e+01  -4.238004
## row67    2.307509  -1.258808  1.831e+00  -0.689860  1.634e+01   3.143694
## row68   -0.872293  -2.960640 -5.254e+00   2.890458  8.343e+00  -0.850989
## row69    1.262893  -2.169212  2.272e+00  -1.928496  2.355e+01  -5.757663
## row70    1.170348  -5.081457 -1.604e+00   3.773581 -2.711e+00   0.812651
## row71   -1.286189   0.182489  1.506e+00   1.191931 -1.202e+00   0.618801
## row72   -1.286189   0.182489  1.506e+00   1.191931 -1.202e+00   0.618801
## row73    1.592292 -10.766912 -2.050e+00   5.448679  1.006e+01   1.906627
## row74    0.603897  -0.921925  5.547e+00 -12.550341  8.165e+00  -7.630364
## row75    2.749752   1.187153  1.044e+00  -0.256609  1.464e+00   7.721069
## row76    2.020781   1.359700  2.244e-01   0.821644 -5.764e-02   2.394571
## row77    1.966777   1.180381  1.817e-01  -0.045764  3.180e-01   4.892474
## row78    1.615087   0.843923  1.066e+00   0.233253  1.345e+00   4.679887
## row79    1.661713   0.932543  9.456e-01   0.298447  1.083e+00   4.250586
## row80    0.907790  -0.035123 -3.192e+00   2.884469  5.221e+00  -1.382564
## row81    1.991517   1.316705  6.749e-01   0.223397  6.468e-02   4.006445
## row82    2.436272   1.627637 -7.700e-01   1.490915  9.038e-01  -0.853407
## row83    1.203791   1.853827 -6.162e-01   1.049202 -1.303e+00  -5.934761
## row84    1.988483   1.481651 -2.499e+00   5.475859 -2.532e+00  -0.732436
## row85   -1.362005   0.341500 -4.000e-01  -1.381851 -1.175e+00   1.183803
## row86    0.372545   0.943640 -1.096e+00   0.825899 -1.005e+00   0.038131
## row87   -1.286189   0.182489  1.506e+00   1.191931 -1.202e+00   0.618801
## row88   -0.667650   0.606831 -7.083e-01  -0.798859 -2.380e-01  -0.714548
## row89   -1.286189   0.182489  1.506e+00   1.191931 -1.202e+00   0.618801
## row90   -0.596629   0.406140  1.246e-01   1.336276 -7.632e-01   1.397892
## row91   -0.086707   0.581486 -5.289e+00  -6.086313 -2.340e-01  -0.550963
## row92    0.018020   0.560682  8.534e-01   1.666565 -1.279e+00   2.702664
## row93   -0.695717   0.517390 -1.921e+00  -2.314471 -9.453e-01  -0.511475
## row94    0.673496   1.671184 -6.339e-01   1.536553 -1.883e+00  -6.783846
## row95   -0.380799  -1.739667  1.199e+00   1.103202  5.403e+00  -0.533653
## row96    0.259359   0.188810 -2.183e-01   1.797141 -6.486e-01  -4.138348
## row97   -0.226392  -2.269629  8.438e-01   1.953240  1.634e+00   2.864758
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## row1585 -1.286189   0.182489  1.506e+00   1.191931 -1.202e+00   0.618801
## row1586 -1.286189   0.182489  1.506e+00   1.191931 -1.202e+00   0.618801
## row1587 -1.286189   0.182489  1.506e+00   1.191931 -1.202e+00   0.618801
## row1588  2.926656 -16.125005 -2.544e+00  -5.743941 -3.438e+01  -8.222299
## row1589  2.174730 -13.105675 -2.265e+00   0.563194 -9.334e+00  -2.514565
## row1590 -1.286189   0.182489  1.506e+00   1.191931 -1.202e+00   0.618801
## row1591  2.455962  -6.737689  7.741e+00 -23.575927  8.726e+00 -15.114723
## row1592 -1.286189   0.182489  1.506e+00   1.191931 -1.202e+00   0.618801
## row1593 -0.535805  -0.594216  4.422e+00  -7.879764  3.213e+00  -4.077428
## row1594  2.449714   0.738136  1.610e+00  -0.420277  2.426e+00   9.844041
## row1595  2.126993   0.991766 -6.820e-01  -2.566980  3.912e+00   3.989673
## row1596  1.231074   0.997345  2.120e-01   0.197557  3.757e+00  -4.518197
## row1597  2.247341   1.026096 -2.227e-01   2.211251  5.627e-01   5.218665
## row1598  0.571021   0.710924 -5.243e-01   0.027733  4.988e-01   2.208192
## row1599  0.782178   0.389980 -7.608e-01   4.024737  8.444e-01   0.963880
## row1600  1.314974   0.708955 -2.894e-01   2.929524  1.404e-01   3.137294
## row1601  2.069453 -12.682938 -2.226e+00   1.446256 -5.828e+00  -1.715424
## row1602  2.410571   2.990772 -2.531e+00   1.842027 -2.486e+00 -13.345591
## row1603 -1.286189   0.182489  1.506e+00   1.191931 -1.202e+00   0.618801
## row1604 -1.286189   0.182489  1.506e+00   1.191931 -1.202e+00   0.618801
## row1605 -1.286189   0.182489  1.506e+00   1.191931 -1.202e+00   0.618801
## row1606 -1.052197   0.360244  1.251e+00   1.233080 -1.283e+00  -0.265097
## row1607 -1.286189   0.182489  1.506e+00   1.191931 -1.202e+00   0.618801
## row1608  2.096643 -12.792119 -2.236e+00   1.218187 -6.734e+00  -1.921819
## row1609  3.399705  -0.655117  3.017e+00  -1.729451  1.088e+01  15.846201
## row1610  0.952781  -6.832762 -7.712e-02  -5.823064  3.081e+00  -1.625667
## 
## 
## Site constraints (linear combinations of constraining variables)
## 
##               CCA1       CCA2      CCA3       CCA4      CCA5       CCA6
## row1     1.4098952 -4.8497337 -1.384125  0.2548256 -1.199678 -0.7107068
## row2    -0.1396282 -2.5357161 -1.390291  1.8857057  2.918085 -0.6382765
## row3    -0.3444270 -2.2743655 -1.868970  1.4582290  1.470042  0.0661155
## row4     0.7849248 -2.5850373 -1.873212  2.2077212 -0.023303 -1.3481891
## row5     1.6274663 -3.7932077 -1.266080  0.7247394  0.154479 -0.5774650
## row6     1.8709570 -2.7256911 -1.201177  1.2212492  1.608536 -0.6697711
## row7    -0.4529415 -2.8322310 -1.946960  1.2281330  0.755566 -0.0687114
## row8    -0.4604390 -2.9201379 -1.670685  1.3593964  0.896601 -0.2529217
## row9    -0.3669850 -2.4257480 -2.198107  1.2888169  1.033598  0.0198197
## row10   -0.3274349 -2.3113750 -2.092211  1.4085053  1.350697 -0.1453553
## row11   -0.4342892 -2.7808333 -2.384483  1.0615661  0.516911 -0.0485038
## row12   -0.3528577 -2.3259323 -1.848000  1.4689458  1.407777  0.0269737
## row13   -0.3548872 -2.4165291 -2.646587  1.0810322  0.788422  0.0213392
## row14   -0.3593349 -2.3479113 -1.945511  1.4113181  1.294182  0.0642545
## row15   -0.2893625 -2.0812823 -3.169773  0.9495896  0.782050  0.2232587
## row16   -0.2893292 -1.9831015 -1.939106  1.5332225  1.731471  0.1733469
## row17   -0.2218520 -2.8583471 -1.397179  1.8123030  2.290765 -0.5510982
## row18   -0.2191261 -2.8577230 -1.396878  1.7412813  2.437364 -0.5554191
## row19   -0.3882824 -2.4725801 -1.885061  1.3782700  1.184634  0.0671922
## row20    1.4023106 -2.8422939 -0.339850 -0.5195354 -1.269660  0.4397831
## row21   -0.3450603 -1.4054786 -0.406401  0.7281854  1.619206  0.5602869
## row22   -0.4818387 -0.8932030 -0.894202  0.4224011  0.561168  1.1408735
## row23    0.6970164 -0.9603257 -0.869046  1.2714230 -0.607208 -0.2341900
## row24    1.5466634 -2.1199392 -0.249959 -0.1911796 -0.380349  0.5700177
## row25    1.6537255 -1.6322246 -0.210740  0.0323280  0.267863  0.5678145
## row26    1.4814693 -1.5402893  0.230324  0.0815518 -0.671370  2.3132222
## row27    1.5847390 -1.3061123  0.140053  0.2353874 -0.204229  1.7431363
## row28    1.7454629 -0.8472868  0.059858  0.4911987  0.572426  1.0245012
## row29    1.8890769 -0.2976049  0.039287  0.7881840  1.376004  0.8669811
## row30    0.9349160  0.4811464 -0.623229  2.0666704  0.754638  0.6931880
## row31    0.8426109  0.1921754 -0.426134  1.8618509 -0.162497 -0.0927746
## row32    0.8064725 -0.0486671 -0.505706  1.6685438 -0.137328 -0.0094173
## row33    0.8100422 -0.2268992 -0.666246  1.6027693 -0.005165 -0.0527011
## row34   -0.5374956 -0.9303794 -0.833718  0.3913788  0.432388  1.8983460
## row35    1.8173816 -0.6656249  0.021193  0.5996674  0.869401  0.5738792
## row36    1.8694354 -0.5610571 -0.014702  0.7627966  0.847465  0.0542135
## row37   -0.3709864 -0.2914225 -1.611100  0.2857705  0.670892  1.5211212
## row38   -0.4290159 -0.7668646 -1.922815  0.0669754  0.017532  1.1048798
## row39   -0.3805291 -0.5028357 -1.651143  0.2577245  0.561090  1.1533513
## row40   -0.5280883 -1.2722619 -1.762198 -0.0430694 -0.439678  0.9428910
## row41   -0.4680156 -0.8503614 -1.584306  0.1279374  0.099525  1.2453218
## row42   -0.4551425 -0.8637289 -1.528052  0.2215242  0.140903  1.0617178
## row43   -0.3408427 -0.2856353 -2.276197  0.0311855  0.322776  1.3743925
## row44   -0.3570928 -0.5043690 -1.991678  0.1723543  0.376110  0.9792095
## row45   -0.4546785 -0.8105019 -2.027098 -0.0514607 -0.172970  1.2945797
## row46   -0.2318655 -1.1236896 -0.513497  1.0442583  1.921147  0.0276049
## row47   -0.5092815 -1.0924832 -0.948419  0.3546232  0.339553  0.9829898
## row48   -0.5427082 -1.2042044 -1.262064  0.1437375 -0.095290  1.1388845
## row49   -0.3695731 -0.3588520 -2.148419  0.0337104  0.263055  1.4739360
## row50   -0.5002365 -0.9875958 -1.808926 -0.0451809 -0.249937  1.3149232
## row51   -0.5574396 -1.2282230 -1.380871  0.0507724 -0.254938  1.2620502
## row52   -0.4854570 -0.8838194 -0.999865  0.3761434  0.441942  1.2180731
## row53   -0.3935498 -0.4830765 -2.471276 -0.1711621 -0.113761  1.5111136
## row54   -0.2914465  0.0732500 -2.878805 -0.1886842  0.201232  1.8141733
## row55   -0.4334336 -0.5465577 -1.176999  0.3744398  0.640907  1.4875069
## row56    1.3771652 -2.9371662 -0.337727 -0.5648871 -1.415289  0.4810649
## row57   -0.2527738 -1.2005235 -0.514263  1.0514105  1.719093  0.0538971
## row58   -0.3193542 -1.3638801 -0.441530  0.7669862  1.726237  0.3998391
## row59   -0.4470483 -0.8694532 -0.960904  0.4679642  0.686070  0.8549360
## row60   -0.3700926 -1.5144543 -0.412803  0.6794938  1.466144  0.5707973
## row61   -0.5300769 -1.1487759 -0.933384  0.3190838  0.237825  1.0647473
## row62    0.6627672 -1.1205166 -0.884621  1.2058553 -0.829756 -0.2441992
## row63    1.5209948 -2.2592470 -0.272701 -0.2475363 -0.553193  0.5226980
## row64    1.6465702 -1.7065417 -0.238233  0.0122270  0.192035  0.4787457
## row65   -0.5417316 -1.2224786 -0.949844  0.2910688  0.153301  1.0212307
## row66    1.4055859 -2.8478506 -0.350666 -0.5175012 -1.261584  0.3965607
## row67   -0.1290065 -0.7183656 -0.513028  1.2453263  2.505444 -0.1081254
## row68   -0.3165044 -1.3704533 -0.451983  0.7686080  1.731786  0.3584958
## row69   -0.4761522 -0.9617941 -0.947955  0.4166756  0.532900  0.9403331
## row70   -0.3356423 -1.4230266 -0.438462  0.7341165  1.640697  0.4325667
## row71   -0.5034707 -1.0217465 -0.919929  0.3725643  0.408607  1.0774352
## row72    0.6727664 -1.0954758 -0.892683  1.2182292 -0.774159 -0.2866029
## row73    1.5668141 -2.0663716 -0.264930 -0.1590213 -0.278545  0.4893004
## row74    1.7077147 -1.4297539 -0.216543  0.1356668  0.568260  0.4748520
## row75    1.7151288 -1.0080468  0.034341  0.4363307  0.350352  0.9737185
## row76    1.6543796 -1.4541955 -0.149021  0.2893824  0.054319  1.0432759
## row77    1.6232892 -1.4847454 -0.054538  0.2427203 -0.192577  0.9929938
## row78    1.7499600 -1.0398568 -0.044148  0.4582727  0.394739  0.4296553
## row79    0.8087145 -0.1654246 -0.659760  1.7659898 -0.183921  0.1914233
## row80    0.8186803 -0.1232827 -0.653165  1.7283417 -0.018677  0.2004177
## row81    0.7968483 -0.2235666 -0.643698  1.5881645 -0.010824  0.1536054
## row82    0.8085157 -0.0868227 -0.527654  1.6004043 -0.038796 -0.0924281
## row83   -0.5058061 -0.6574759 -0.664658  0.4644178  0.467351  1.6006788
## row84    1.7889867 -0.9009882 -0.031954  0.6410102  0.301711  0.1006989
## row85   -0.4718301 -0.2794189 -2.171799  0.4637036 -0.152735  0.6481099
## row86   -0.1797184  1.0875260 -2.661437  0.7749087  1.186702  0.8569872
## row87   -0.0730724  1.6512293 -5.006349 -0.2200075  0.156227  1.5715469
## row88   -0.4199804  0.2980705 -1.058269  1.0854855  1.027183  1.1690260
## row89   -0.4706593 -0.3224801 -0.878448  1.0977411  0.812460  0.2538810
## row90   -0.3405775  0.5123573 -1.228230  1.1714189  1.323007  0.8788584
## row91   -0.3740350  0.2397967 -2.343319  0.5601233  0.300011  0.8577588
## row92   -0.3782792  0.4136831 -0.764889  1.3257851  1.452775  0.9362799
## row93   -0.3788898  0.1826919 -1.847200  0.8022236  0.623302  0.6671340
## row94   -0.2898039  0.6342985 -2.475158  0.6579569  0.687138  0.9156655
## row95   -0.3010498 -0.7795953 -0.367586  1.5725371  1.909557 -0.5667870
## row96   -0.5822900 -0.7091298 -0.774315  0.9317953  0.256678  0.4959971
## row97   -0.3759721 -0.8271797 -0.214321  1.3857805  1.808218  0.0814070
## row98   -0.5564880 -0.6010532 -0.769694  0.9748640  0.423341  0.4779107
## row99    0.6163986 -0.6398414 -0.714376  1.8272204 -0.754429 -0.7807838
## row100   1.5069584 -1.6218238 -0.084777  0.4401829 -0.270453  0.0063232
## row101   1.6974769 -0.8491528 -0.071549  0.8237124  0.813340 -0.2005469
## row102   1.2950048 -2.5514760 -0.140823 -0.0002644 -1.521322  0.0880988
## row103  -0.3009294 -0.8236143 -0.393460  1.5595487  1.889860 -0.6599404
## row104  -0.3811760 -0.9531293 -0.276700  1.3565659  1.707598 -0.1355348
## row105  -0.5314207 -0.5194766 -0.779658  1.0196326  0.556228  0.4086322
## row106  -0.4219059 -0.9759900 -0.196210  1.3103341  1.553197  0.2079808
## row107  -0.5975901 -0.6245146 -0.688768  0.9289419  0.265779  0.8235094
## row108   0.5765658 -0.6729950 -0.642284  1.7829154 -0.917995 -0.4685470
## row109   1.4871615 -1.6599483 -0.061587  0.4123385 -0.362788  0.1160917
## row110   1.6941003 -0.6830298  0.030649  0.8957806  0.829446  0.1718717
## row111  -0.5766563 -0.7352331 -0.443900  1.1023115  0.535015  0.3084908
## row112  -0.5351125 -0.4990908 -0.808896  1.0066660  0.500606  0.4951975
## row113  -0.5026746 -0.3036520 -1.188341  0.8760782  0.420886  0.6892832
## row114  -0.4923364 -0.1960001 -0.878105  1.0413188  0.724450  0.7574586
## row115  -0.5351487 -0.4956654 -1.203846  0.8099577  0.213544  0.5917924
## row116  -0.5165634 -0.2840509 -0.650300  1.1041041  0.758546  0.7557277
## row117  -0.4254724 -0.0170355 -1.863534  0.6940579  0.361782  0.6988798
## row118  -0.4465774  0.0423952 -1.051698  1.0339980  0.878487  0.8680876
## row119  -0.4995182 -0.3560341 -1.268780  0.8487983  0.365849  0.5572057
## row120   1.7193319 -0.5545603  0.030449  1.1205614  0.688131  0.1755430
## row121   1.6636049 -0.6610301  0.136429  1.0403122  0.295649  0.1996950
## row122   1.5949246 -0.7668911  0.263397  0.9380188 -0.090187  0.4240597
## row123   1.6940156 -0.4598031  0.247092  1.0865723  0.369543 -0.0907150
## row124   0.7253910  0.4528294 -0.223829  2.3864249 -0.507184 -0.4189046
## row125   0.8097145  0.4712219 -0.488635  2.4887223  0.044873 -0.6203901
## row126   0.7071618  0.1938069 -0.396238  2.2168867 -0.312077 -0.2616921
## row127   0.7372780  0.2027827 -0.444783  2.1824902 -0.113188 -0.5856219
## row128  -0.5586949 -0.3043450 -0.533825  1.0447599  0.386857  0.7156667
## row129   1.8130634 -1.8403813 -1.722861  1.1754387  2.390135  1.9480014
## row130  -0.3833087  0.1922117 -1.814394  0.1732841  0.337666  0.8661842
## row131  -0.3978475  0.1899387 -0.737451  0.6773601  1.046863  0.7670723
## row132  -0.3732974  0.3521242 -1.386066  0.3958257  0.729270  1.0275637
## row133  -0.4200764  0.1770432 -0.847182  0.5702659  0.860109  0.9896255
## row134  -0.3189255  0.3920294 -1.288899  0.5515269  1.098098  0.5462005
## row135  -0.2879348  0.7365360 -0.838796  0.8312508  1.620350  0.9000459
## row136  -0.3361868  0.5469056 -0.566020  0.8760367  1.539197  0.9026897
## row137  -0.3040792  0.5422713 -1.726402  0.3891485  0.823443  0.8211500
## row138  -0.2142443  0.9233694 -1.785859  0.5190704  1.318842  0.7808003
## row139  -0.2843766 -0.5788753 -0.047242  1.0210319  2.141526 -0.1893084
## row140  -0.4424179 -0.1519084 -0.536117  0.6743297  0.959972  0.4158519
## row141   0.6589105 -0.4358113 -0.460274  1.4047536 -0.620342 -0.6733120
## row142   1.5718378 -1.3307750  0.169074  0.0575443 -0.003227  0.0829264
## row143   1.8093389 -0.2443624  0.255255  0.5954993  1.361270  0.0760655
## row144  -0.2825330 -0.6452989 -0.098099  1.0979462  1.942020 -0.3722662
## row145  -0.3359216 -0.7415228 -0.024518  0.9391411  1.854598 -0.0386121
## row146  -0.4730958 -0.2300328 -0.511915  0.6333455  0.793680  0.5439670
## row147  -0.3273196 -0.7458458 -0.047125  0.9495931  1.876707 -0.1312357
## row148  -0.4295908 -0.1993417 -0.594281  0.6850605  0.960606  0.1900270
## row149  -0.2944397 -0.3611538  0.103563  1.0638879  2.228108  0.3657943
## row150  -0.5011914 -0.2061266 -0.432875  0.6079498  0.715151  0.8653238
## row151   1.5122616 -1.4869516  0.214241 -0.0324204 -0.311462  0.3249227
## row152   1.8349627 -0.0302323  0.370803  0.7654239  1.204617 -0.1533276
## row153   1.8292333 -0.0545397  0.339523  0.7563756  1.269003  0.0652754
## row154   1.8613935 -0.0216678  0.254634  0.7964619  1.501889  0.0406444
## row155   1.8226369 -0.0936907  0.301213  0.7467619  1.314853  0.2598781
## row156   0.8881912  0.7647625 -0.258712  2.0495018  0.491755 -0.6495829
## row157   0.8915167  0.8435416 -0.169345  2.0622050  0.394278 -0.8719997
## row158   0.8529417  0.7380130 -0.173718  2.0149134  0.272631 -0.5125330
## row159   0.8360113  0.5645449 -0.287112  1.9643113  0.272334 -0.3582710
## row160  -0.5112509  0.0523452 -0.163463  0.6866071  0.445203  0.8036810
## row161   1.8170796 -0.0641941  0.467429  0.9147346  0.490804 -0.7479149
## row162  -0.4733011 -0.2144355 -1.271015  0.2880913  0.184803  0.7415836
## row163  -0.4220941  0.1872969 -0.433171  0.7854444  1.128107  0.9361506
## row164  -0.5204255 -0.4377747 -0.918976  0.3778726  0.160082  0.6392024
## row165  -0.5464706 -0.5480045 -0.560973  0.5020873  0.277477  0.5772379
## row166  -0.3464207  0.5220809 -0.301894  0.9929862  1.664478  0.8898307
## row167  -0.4033201  0.1120852 -1.323750  0.4073192  0.531053  0.7714343
## row168  -0.3279613  0.7623743 -0.218548  1.0630073  1.850905  1.2213625
## row169  -0.1958313  1.1608070 -1.949754  0.4969252  1.271907  1.1530743
## row170   1.4205683 -1.9999137  0.126354 -0.2652213 -0.886073  0.1313491
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## row1551  0.1868731  0.0139145  0.120034  1.6384783 -2.116963 -0.7951776
## row1552  1.0925085 -0.8929672  0.786127  0.2929854 -1.509705  0.0004776
## row1553  1.1439669 -0.6753562  0.643300  0.3264500 -1.327686 -0.0035220
## row1554  0.2464304  0.2827244  0.473789  1.2961726 -1.809100 -0.7370684
## row1555  1.1615782 -0.5800152  0.878960 -0.1566691 -1.343984  0.1182478
## row1556 -0.9391065  0.2936480  0.393063  0.3995226 -0.708618  0.5948550
## row1557  1.5091269  0.9652596  0.477061  0.3978984  0.180715  0.0705435
## row1558  1.4937648  0.8813449  0.525308  0.3932702  0.125116  0.0276243
## row1559  1.4582292  0.6381275  0.546532  0.3397738 -0.075359 -0.1611581
## row1560  0.5288141  1.4075603 -0.223639  1.6162940 -0.745467 -0.7237836
## row1561  0.5329482  1.5367803 -0.148358  1.6083904 -0.920334 -0.9766954
## row1562  0.5492645  1.6446748 -0.199897  1.6233979 -0.778068 -0.7502969
## row1563  0.5339843  1.5157598 -0.202133  1.6354880 -0.693455 -0.5397528
## row1564  1.0494202 -1.2119334  1.057381 -0.2921379 -1.851176 -0.1945963
## row1565 -0.7281603  0.0605465  0.589831  0.7098293  0.550431 -0.0486357
## row1566 -0.9449936  0.1989592  0.213237  0.3134180 -0.901835  0.4798029
## row1567  0.1961240 -0.0157901  0.332982  1.1440053 -2.229669 -0.8666490
## row1568  1.1429493 -0.7150786  0.878266 -0.1693932 -1.494464 -0.0009231
## row1569 -0.8133734 -0.4039020  0.820618  0.6784183  0.193657 -0.2797637
## row1570  0.9781533 -1.5572662  1.083020 -0.4060881 -2.261639 -0.2532955
## row1571 -0.9291615 -0.9380155  0.637190  0.3746965 -0.624290 -0.2628619
## row1572 -1.1184715 -0.6094245  0.289339  0.0352688 -1.876429  0.4076388
## row1573  0.0946977 -0.5479901  0.348131  0.9725000 -2.833542 -1.0362940
## row1574  1.7299167  0.3691110  0.380605  1.1500693  0.144508  1.1439390
## row1575  1.6945195  0.2788222  0.473779  1.0825089 -0.059482  1.0789218
## row1576  1.6878268  0.2333786  0.544337  1.0643794 -0.128243  0.8280657
## row1577  0.7166773  0.8386426 -0.057168  2.3439981 -0.913746  0.2830932
## row1578  0.6866387  0.6367005 -0.087886  2.3079573 -0.975573  0.4169224
## row1579  0.6446162  0.3687286 -0.019956  2.2957995 -0.981457  0.5741176
## row1580  0.6537176  0.3998678  0.109623  2.3605808 -0.905880  0.3855809
## row1581 -0.6114195 -0.9551691  0.822391  1.3564896  0.225759  1.0147998
## row1582  0.3595334 -0.8813193  0.485740  1.8370115 -2.340362  0.0796570
## row1583 -0.5611040 -0.8680415  0.834679  1.4628421  0.511519  0.6980852
## row1584  1.2245975 -2.0609189  1.120331  0.4072646 -2.010103  0.6820136
## row1585 -0.7857312 -0.8579866  1.008163  0.9207256  0.740550  0.2237827
## row1586 -0.9819120 -0.5465660  0.547149  0.5181446 -0.643698  0.9488642
## row1587  0.2313370 -0.4600289  0.496241  1.3924441 -1.664328 -0.4130447
## row1588  1.1794691 -1.2405040  1.227970  0.1409541 -0.732908  0.2267731
## row1589  1.1151417 -1.4929860  1.131551 -0.0027263 -1.219538  0.3269196
## row1590 -0.8302519 -0.9162294  0.955642  0.8131351  0.445898  0.5531974
## row1591  1.0855135 -1.4948469  1.182619 -0.0038177 -1.398868  0.6009602
## row1592  0.1870943 -0.6378348  0.508113  1.3157111 -1.913472 -0.3661399
## row1593 -0.8143397 -1.0739207  0.881285  0.8160439  0.456263  0.0564915
## row1594  1.2978172 -0.7211647  0.352682  0.1377445 -1.024848  0.3498301
## row1595  1.2128998 -1.0626953  0.495118  0.0413802 -1.351177  0.4858847
## row1596  1.2093529 -1.0385862  0.491575 -0.0217670 -1.328544  0.5205755
## row1597  0.3561529  0.2424203 -0.647752  1.0983150 -2.165915 -0.3362619
## row1598  0.3351199 -0.1240138 -0.144259  1.3718922 -1.442452 -0.2182960
## row1599  0.3000572 -0.6144025 -0.280688  1.3809835 -1.056695  0.3826929
## row1600  0.2734628 -0.5787707 -0.111450  1.3375278 -1.398137  0.0747617
## row1601  1.0661816 -1.7360463  1.103264 -0.1016874 -1.538901  0.2833396
## row1602  1.0471384 -1.8538641  1.040830 -0.1426140 -1.741431  0.2195742
## row1603 -0.8479424 -1.0366868  0.804147  0.7711834  0.116065  0.4783086
## row1604 -0.8500427 -1.1334620  0.902128  0.7558784  0.274090  0.2795018
## row1605 -0.9472957 -1.5253324  0.926925  0.5906845 -0.281650  0.3794476
## row1606  0.1256991 -0.8642147  0.383099  1.1525174 -2.384631 -0.2279689
## row1607 -1.1243216 -1.1430920  0.428301  0.2005880 -1.574078  1.0791166
## row1608  1.0671535 -1.6818312  1.099151 -0.1024564 -1.532860  0.3951514
## row1609  1.1146348 -1.5424359  1.062711  0.0298561 -1.391293  0.2181981
## row1610  1.1069364 -1.3262685  0.369936 -0.3976047 -1.810524  0.9509688
## 
## 
## Biplot scores for constraining variables
## 
##                          CCA1     CCA2     CCA3      CCA4       CCA5     CCA6
## Cond                -0.117619  0.22693  0.25706  0.416061 -0.1506079 -0.08766
## WTemp                0.038643  0.37088 -0.17335 -0.009927  0.2804837 -0.16995
## SecDepth            -0.200444 -0.06514  0.12341  0.062720  0.0294296 -0.02608
## Turb                 0.248145  0.37962 -0.74633 -0.183637  0.0179697  0.17087
## DOx                 -0.369419 -0.15201  0.02407 -0.189158 -0.2869284  0.36434
## WYTypeC             -0.231771  0.20818  0.29458 -0.141069 -0.0610973 -0.23661
## WYTypeD              0.046539  0.08517  0.18264 -0.321318  0.1665982  0.04898
## WYTypeW              0.284486 -0.26470 -0.26487  0.483691  0.0546413  0.41425
## ActionPhaseDuring   -0.044047  0.24752  0.03555  0.124087  0.0544190 -0.25556
## ActionPhasePost      0.088072  0.02015  0.27277  0.093048 -0.0506486  0.24158
## FlowPulseTypeMA-Ag  -0.030423 -0.04067  0.18255  0.202802 -0.1832027 -0.01240
## FlowPulseTypeMA-SR  -0.037563  0.02918 -0.24947 -0.028772 -0.0872875 -0.23922
## FlowPulseTypeNF     -0.008808 -0.03252  0.11849  0.021575  0.2575866  0.13455
## Month.L              0.105727  0.15753  0.44508  0.047691 -0.0006106  0.30646
## Month.Q              0.125203 -0.31039 -0.09590  0.124429  0.0812208  0.08044
## Month.C             -0.051754 -0.14461 -0.29420  0.055514 -0.1081123  0.10608
## Month^4             -0.043859  0.28762 -0.02163 -0.070557 -0.2064611  0.22501
## Month^5             -0.030428 -0.01385  0.07113  0.075663  0.0313348 -0.20011
## RegionCentralYolo    0.848411 -0.13670  0.20310 -0.324753  0.0614219  0.05753
## RegionLowerSacRiver -0.413952 -0.09856  0.30189  0.275661  0.2818543 -0.17123
## RegionLowerYolo      0.189677  0.25997 -0.13306  0.386443 -0.3797470 -0.30779
## 
## 
## Centroids for factor constraints
## 
##                              CCA1      CCA2     CCA3      CCA4      CCA5
## WYTypeBN                 -0.17647  0.048585 -0.16155 -0.245828 -0.165890
## WYTypeC                  -0.43526  0.390952  0.55320 -0.264922 -0.114738
## WYTypeD                   0.13718  0.251037  0.53834 -0.947101  0.491057
## WYTypeW                   0.37557 -0.349444 -0.34968  0.638557  0.072136
## ActionPhasePre           -0.04792 -0.377356 -0.39304 -0.293321 -0.013814
## ActionPhaseDuring        -0.05344  0.300283  0.04313  0.150541  0.066020
## ActionPhasePost           0.15239  0.034866  0.47197  0.161002 -0.087638
## FlowPulseTypeCA           0.11555  0.101787 -0.24790 -0.339457 -0.170234
## FlowPulseTypeMA-Ag       -0.07141 -0.095470  0.42850  0.476047 -0.430042
## FlowPulseTypeMA-SR       -0.12341  0.095856 -0.81964 -0.094530 -0.286786
## FlowPulseTypeNF          -0.00816 -0.030125  0.10978  0.019988  0.238645
## Month6                    0.37335 -1.268759 -2.95658 -0.609195  0.595966
## Month7                   -0.22069 -1.364878 -0.99321  0.434051  0.404732
## Month8                   -0.03986  0.135148 -0.14606 -0.100079 -0.144112
## Month9                   -0.07633  0.340913  0.28231 -0.008719 -0.066093
## Month10                   0.16673 -0.086695  0.47902 -0.030970  0.330074
## Month11                   0.81082 -0.566422  0.50312  1.171646 -0.917492
## RegionCacheSloughComplex -0.84781  0.008399 -0.50148 -0.354650  0.001371
## RegionCentralYolo         1.38106 -0.222519  0.33060 -0.528637  0.099983
## RegionLowerSacRiver      -0.77813 -0.185259  0.56747  0.518174  0.529815
## RegionLowerYolo           0.40999  0.561918 -0.28761  0.835292 -0.820819
##                              CCA6
## WYTypeBN                 -0.37304
## WYTypeC                  -0.44435
## WYTypeD                   0.14437
## WYTypeW                   0.54688
## ActionPhasePre            0.06020
## ActionPhaseDuring        -0.31005
## ActionPhasePost           0.41800
## FlowPulseTypeCA           0.01802
## FlowPulseTypeMA-Ag       -0.02911
## FlowPulseTypeMA-SR       -0.78597
## FlowPulseTypeNF           0.12466
## Month6                   -1.90466
## Month7                   -1.22958
## Month8                    0.22543
## Month9                   -0.16103
## Month10                  -0.08396
## Month11                   3.50201
## RegionCacheSloughComplex  0.49413
## RegionCentralYolo         0.09365
## RegionLowerSacRiver      -0.32187
## RegionLowerYolo          -0.66528

Interpretation

  1. Interpretation of CCA axis, terms
  • global model
  • axis
  • terms (order matters)
  • Can use a step model to create final CCA model
# Test the significance of the CCA
anova(spe.cca)
## Permutation test for cca under reduced model
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = seine.sp ~ Cond + WTemp + SecDepth + Turb + DOx + WYType + ActionPhase + FlowPulseType + Month + Region, data = seine.env.f)
##            Df ChiSquare      F Pr(>F)    
## Model      21   0.45012 13.612  0.001 ***
## Residual 1588   2.50057                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
anova(spe.cca, by = "axis")
## Permutation test for cca under reduced model
## Forward tests for axes
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = seine.sp ~ Cond + WTemp + SecDepth + Turb + DOx + WYType + ActionPhase + FlowPulseType + Month + Region, data = seine.env.f)
##            Df ChiSquare        F Pr(>F)    
## CCA1        1   0.23500 150.1778  0.001 ***
## CCA2        1   0.10254  65.5290  0.001 ***
## CCA3        1   0.04697  30.0148  0.001 ***
## CCA4        1   0.01697  10.8465  0.001 ***
## CCA5        1   0.01446   9.2403  0.003 ** 
## CCA6        1   0.01227   7.8424  0.012 *  
## CCA7        1   0.00793   5.0680  0.322    
## CCA8        1   0.00732   4.6768  0.372    
## CCA9        1   0.00374   2.3906  0.996    
## CCA10       1   0.00225   1.4370  1.000    
## CCA11       1   0.00067   0.4267  1.000    
## Residual 1598   2.50057                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
anova(spe.cca, by = "terms")
## Permutation test for cca under reduced model
## Terms added sequentially (first to last)
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = seine.sp ~ Cond + WTemp + SecDepth + Turb + DOx + WYType + ActionPhase + FlowPulseType + Month + Region, data = seine.env.f)
##                 Df ChiSquare       F Pr(>F)    
## Cond             1   0.01641 10.4233  0.001 ***
## WTemp            1   0.01817 11.5391  0.001 ***
## SecDepth         1   0.01013  6.4362  0.001 ***
## Turb             1   0.04757 30.2125  0.001 ***
## DOx              1   0.03784 24.0332  0.001 ***
## WYType           3   0.03635  7.6951  0.001 ***
## ActionPhase      2   0.04705 14.9384  0.001 ***
## FlowPulseType    3   0.01794  3.7975  0.001 ***
## Month            5   0.04407  5.5971  0.001 ***
## Region           3   0.17458 36.9552  0.001 ***
## Residual      1588   2.50057                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
anova(spe.cca, by = 'margin')
## Permutation test for cca under reduced model
## Marginal effects of terms
## Permutation: free
## Number of permutations: 999
## 
## Model: cca(formula = seine.sp ~ Cond + WTemp + SecDepth + Turb + DOx + WYType + ActionPhase + FlowPulseType + Month + Region, data = seine.env.f)
##                 Df ChiSquare       F Pr(>F)    
## Cond             1   0.01137  7.2189  0.001 ***
## WTemp            1   0.03187 20.2370  0.001 ***
## SecDepth         1   0.00196  1.2424  0.227    
## Turb             1   0.03110 19.7505  0.001 ***
## DOx              1   0.00738  4.6869  0.001 ***
## WYType           3   0.04176  8.8402  0.001 ***
## ActionPhase      2   0.01041  3.3061  0.001 ***
## FlowPulseType    3   0.01534  3.2475  0.001 ***
## Month            5   0.03669  4.6597  0.001 ***
## Region           3   0.17458 36.9552  0.001 ***
## Residual      1588   2.50057                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Forward stepping
cca.step <- ordistep(cca(seine.sp ~ 1, data = seine.env.f), scope = formula(spe.cca), 
                        direction = "forward", pstep = 1000)
## 
## Start: seine.sp ~ 1 
## 
##                 Df    AIC       F Pr(>F)   
## + Region         3 2359.0 49.2542  0.005 **
## + Turb           1 2465.6 31.4198  0.005 **
## + WYType         3 2472.6  9.4504  0.005 **
## + DOx            1 2475.4 21.4291  0.005 **
## + Month          5 2476.2  5.7275  0.005 **
## + WTemp          1 2486.9  9.8683  0.005 **
## + ActionPhase    2 2487.0  5.8779  0.005 **
## + Cond           1 2487.8  8.9946  0.005 **
## + SecDepth       1 2490.6  6.1428  0.005 **
## + FlowPulseType  3 2493.7  2.3581  0.005 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Step: seine.sp ~ Region 
## 
##                 Df    AIC       F Pr(>F)   
## + Turb           1 2335.7 25.4795  0.005 **
## + Month          5 2341.7  5.4886  0.005 **
## + WYType         3 2342.8  7.4248  0.005 **
## + WTemp          1 2350.8 10.2736  0.005 **
## + Cond           1 2351.9  9.0765  0.005 **
## + ActionPhase    2 2352.1  5.4799  0.005 **
## + DOx            1 2355.2  5.8087  0.005 **
## + FlowPulseType  3 2357.5  2.5164  0.005 **
## + SecDepth       1 2359.0  2.0408  0.070 . 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Step: seine.sp ~ Region + Turb 
## 
##                 Df    AIC      F Pr(>F)   
## + WYType         3 2319.0 7.5629  0.005 **
## + Month          5 2319.3 5.2920  0.005 **
## + ActionPhase    2 2328.6 5.5314  0.005 **
## + Cond           1 2328.6 9.0207  0.005 **
## + WTemp          1 2328.8 8.8942  0.005 **
## + DOx            1 2333.0 4.6301  0.005 **
## + FlowPulseType  3 2336.4 1.7379  0.025 * 
## + SecDepth       1 2336.9 0.7485  0.630   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Step: seine.sp ~ Region + Turb + WYType 
## 
##                 Df    AIC      F Pr(>F)   
## + Month          5 2302.7 5.2710  0.005 **
## + ActionPhase    2 2310.1 6.4696  0.005 **
## + WTemp          1 2313.6 7.4466  0.005 **
## + Cond           1 2314.1 6.8798  0.005 **
## + FlowPulseType  3 2315.1 3.2973  0.005 **
## + DOx            1 2315.9 5.0778  0.005 **
## + SecDepth       1 2320.1 0.9112  0.460   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Step: seine.sp ~ Region + Turb + WYType + Month 
## 
##                 Df    AIC       F Pr(>F)   
## + WTemp          1 2284.6 20.0350  0.005 **
## + Cond           1 2298.1  6.5435  0.005 **
## + FlowPulseType  3 2298.7  3.3166  0.005 **
## + ActionPhase    2 2299.9  3.3728  0.005 **
## + DOx            1 2299.9  4.7293  0.005 **
## + SecDepth       1 2303.5  1.1985  0.255   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Step: seine.sp ~ Region + Turb + WYType + Month + WTemp 
## 
##                 Df    AIC      F Pr(>F)   
## + Cond           1 2279.5 7.0339  0.005 **
## + FlowPulseType  3 2280.9 3.2168  0.005 **
## + ActionPhase    2 2281.0 3.7848  0.005 **
## + DOx            1 2281.7 4.8599  0.005 **
## + SecDepth       1 2285.4 1.1592  0.335   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Step: seine.sp ~ Region + Turb + WYType + Month + WTemp + Cond 
## 
##                 Df    AIC      F Pr(>F)   
## + FlowPulseType  3 2275.2 3.4153  0.005 **
## + ActionPhase    2 2276.1 3.6893  0.005 **
## + DOx            1 2276.7 4.7404  0.005 **
## + SecDepth       1 2280.3 1.1853  0.315   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Step: seine.sp ~ Region + Turb + WYType + Month + WTemp + Cond + FlowPulseType 
## 
##               Df    AIC      F Pr(>F)   
## + DOx          1 2272.0 5.1585  0.005 **
## + ActionPhase  2 2272.3 3.4221  0.005 **
## + SecDepth     1 2276.1 1.0563  0.330   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Step: seine.sp ~ Region + Turb + WYType + Month + WTemp + Cond + FlowPulseType +      DOx 
## 
##               Df    AIC      F Pr(>F)   
## + ActionPhase  2 2269.5 3.1931  0.005 **
## + SecDepth     1 2272.9 1.0143  0.430   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Step: seine.sp ~ Region + Turb + WYType + Month + WTemp + Cond + FlowPulseType +      DOx + ActionPhase 
## 
##            Df    AIC      F Pr(>F)
## + SecDepth  1 2270.2 1.2424   0.25

Plot

  1. Plot CCA
plot(spe.cca, choices = c(1,2), display = c('wa', 'sp', 'bp'), scaling = 2)

# Plot the CCA

cca.biplot = function(cca){
  
  #find plot dimensions (changed these so all the points would fit)
  xmin = min(summary((cca))$species[, 1]) * 1.6
  xmax = max(summary((cca))$species[, 1]) * 1.4
  ymin = min(summary((cca))$species[, 2]) * 1.2
  ymax = max(summary((cca))$species[, 2]) * 2.2
  
  par(bty='l')
  
  # plot(cca,disp='species',scaling=1) #scale to show species the best
  plot(summary((cca))$species[, 1], summary((cca))$species[, 2],
       type = 'n', xlim = c(xmin, xmax), ylim = c(ymin, ymax), 
       ylab = 'CA2 (8.0% Variation Explained)', xlab = 'CA1 (3.5% Variation Explained)')
  axis(side = 1, lwd = 2)
  axis(side = 2, lwd = 2)
  box(lwd = 2)
  
  #draw origin lines
  segments(-2, 0, 2, 0, lwd = 1, lty = 3)
  segments(0, -4, 0, 2, lwd = 1, lty = 3)
  
  #Add species names
  text(summary((cca))$species[, 1],summary((cca))$species[, 2], labels = rownames(summary((cca))$species), cex = 0.8)
  
  #define continuous variables possibly used
  cont.vars=c('Cond','WTemp','DOx','SecDepth','Turb')
  
  bi.names = row.names(summary(cca)$biplot) #names of environmental variables
  # centroid.names=row.names(summary(cca)$centroid) 
  centroid.names = data.frame(Rows = rownames(summary((cca))$centroid))
  
  #Pain in the a$$ way to do this, but I created abbreviated names for each level of
  #my categorical variable so that they would look nicer when plotted
  #Else I would have names like HabitatC on the biplot
  # 
  centroid.names$New[centroid.names$Rows == 'ActionPhasePre'] = 'PreAction'
  centroid.names$New[centroid.names$Rows == 'ActionPhaseDuring'] = 'DuringAction'
  centroid.names$New[centroid.names$Rows == 'ActionPhasePost'] = 'PostAction'

  centroid.names$New[centroid.names$Rows == 'WYTypeC'] = 'CriticalWY'
  centroid.names$New[centroid.names$Rows == 'WYTypeD'] = 'DryWY'
  centroid.names$New[centroid.names$Rows == 'WYTypeW'] = 'WetWY'

  centroid.names$New[centroid.names$Rows == 'FlowPulseTypeMA-Ag'] = 'AgPulse'
  centroid.names$New[centroid.names$Rows == 'FlowPulseTypeMA-SR'] = 'SRPulse'
  centroid.names$New[centroid.names$Rows == 'FlowPulseTypeNF'] = 'NoFA'
  
  centroid.names$New[centroid.names$Rows == 'Month4'] = 'Apr'
  centroid.names$New[centroid.names$Rows == 'Month5'] = 'May'
  centroid.names$New[centroid.names$Rows == 'Month6'] = 'June'
  centroid.names$New[centroid.names$Rows == 'Month7'] = 'July'
  centroid.names$New[centroid.names$Rows == 'Month8'] = 'Aug'
  centroid.names$New[centroid.names$Rows == 'Month9'] = 'Sep'
  centroid.names$New[centroid.names$Rows == 'Month10'] = 'Oct'
  centroid.names$New[centroid.names$Rows == 'Month11'] = 'Nov'
  centroid.names$New[centroid.names$Rows == 'Month12'] = 'Dec'
  centroid.names$New[centroid.names$Rows == 'Month1'] = 'Jan'
  centroid.names$New[centroid.names$Rows == 'Month2'] = 'Feb'
  centroid.names$New[centroid.names$Rows == 'Month3'] = 'Mar'
  
  
  #This could possibly be slimmed down, but it plots arrows if the variable is continuous (part of the list above)
  # and plots a point for the categorical variables instead
  
  for(i in 1:length(summary(cca)$biplot[, 1])){
    
    #Test that the row name is one of the continuous variables before plotting arrows
    if(bi.names[i] %in% cont.vars){
      arrows(0, 0, summary(cca)$biplot[i, 1], summary(cca)$biplot[i, 2],
             lwd = 1, angle = 25, length = 0.10, col = "#F4aa42")
      text(summary(cca)$biplot[i, 1] * 1.5, 
           summary(cca)$biplot[i, 2] * 1.5, labels = bi.names[i], col = '#F4aa42', cex = 0.8, font = 4)
    }
    
  }
  
  #now plot the centered mean value of each nominal variable
  #Use if statement to test for case where I don't have any categorical variables
  
  if(is.numeric(summary(cca)$centroids) == TRUE){
    
    points(summary(cca)$centroids[, 1] * 0.9, summary(cca)$centroids[, 2] * 0.9, pch = 15, col = 'black')
    
    text(summary(cca)$centroids[, 1] * 0.9, (summary(cca)$centroids[, 2] * 0.9 + 0.15), labels = centroid.names$New,
         col = 'darkcyan', cex = 0.7, adj = .5)
  }
  
}

cca.biplot(spe.cca)